AP CALC by Jim Cho

jcho11 — 2021-01-31 19:56:54 UTC

jcho11 — 2021-01-31 19:57:56 UTC

dena_meseret — 2021-02-01 21:12:57 UTC

Will try to find out more than one way to find the solution. I also want to work on the way I explain answers, it should be more formal. Questions: Will we work on AP Classroom this module? Could we have earlier to access slides, because I would like to preview them before class and ask questions? What are the topics we will be learning this module?

Guadalupe Baltazar

guadalupe_baltazar — 2021-02-01 21:12:58 UTC

I would stay on track by taking more notes, collaboration, and deeply analyze the mistakes I did in order to grow from it.

ashley_laraharo — 2021-02-01 21:13:00 UTC

I will try to focus on not being afraid to make mistakes (a big challenge I have), correct them, and ask for help. Also to think creatively in order to justify my mathematical reasoning.

diego_barcenas1 — 2021-02-01 21:13:05 UTC

I will try to focus on noticing patterns and seeing where a rule comes from in terms of logic. A challenge would be to come up with a perfectly described solution, as I have to apply various aspects of calculus to the real world.

elyna_dotimas — 2021-02-01 21:13:10 UTC

I want to focus on collaborating with a group and working together to come up with an answer. Also just viewing all questions as a divergent thinker. The biggest challenge for me will be breaking the norm that there is only one answer and only one way to get there.

I will try to focus on understanding the problem and my mistakes. - Megha

2021-02-01 21:13:17 UTC

chloeannemhari_reyes — 2021-02-01 21:13:21 UTC

I want to focus on understanding how the math we do relates to the real world. More specifically, I want to challenge myself to see how it can relate to my own life.

Jasmine

2021-02-01 21:13:30 UTC

I will try to focus on finding consistencies with each problem.

Jose Miguel

jose_romero16 — 2021-02-01 21:13:30 UTC

I'll try to focus on being able to see patterns and finding the correct way to apply math to different scenarios. I think the biggest challenge will be figuring out what math I will have to use for the word problems and scenarios.

Jennifer

jennifer_macy — 2021-02-01 21:13:33 UTC

I am going to try focusing on better explaining my work and what I am showing through my work. Along with asking for help more often when I need it.

sruthy_sabesan — 2021-02-01 21:13:48 UTC

Goals to Focus on This Semester:
- asking more questions
- if something is not clear, I'll take the time out of class to understand it better for myself
- group collaboration and communication

Questions:
- What will we cover in this unit?
- What should we do during the units we don't have this class?

Gabby A.

2021-02-01 21:13:49 UTC

One goal would be to have thorough explanations for justifications from my work. This will help as peers won't have to ask for how I did something, my thorough explanations will be enough.

Hailee

hailee_ballardocazatt — 2021-02-01 21:14:14 UTC

andrea_ramirez32 — 2021-02-01 21:14:20 UTC

I want to focus on understanding the problem and being open to what the different solutions can be.

Ryan T.

2021-02-01 21:14:23 UTC

my goal is to get my work done when its assigned instead of letting it all build up

tehzeeb_siddiqui — 2021-02-01 21:14:25 UTC

I want to focus on being able to explain my thought process and the steps i took to get an answer, because then i'll be able to defend my work.

I will focus on making sure I justify my answers.

sebastian_carranza — 2021-02-01 21:14:25 UTC

I want to try better explaining the math more accurately, so what I say makes sense.

kiane_souvannavong — 2021-02-01 21:14:41 UTC

Armando A

2021-02-01 21:14:47 UTC

I want to focus on my time management. My goal is to turn in all of my homework on time.

Jannelle

jannelle_aquino — 2021-02-01 21:16:07 UTC

I will try to focus more on why any math answer is correct and how the answer came to be so I can be able to explain to others and understand more of the content for myself.

prinay_singh — 2021-02-01 21:17:12 UTC

Prinay- My goals I will focus on this semester are I would try to explain more of my thoughts of the questions in class and be more confident in myself so I can become better as a student.

dena_meseret — 2021-02-01 21:21:54 UTC

Notice:
-Min/Maxs
-There are inflection points
Wonders:
-Are the mins/maxs considered inflection points?

ashley_laraharo — 2021-02-01 21:22:11 UTC

I notice that curve sketching is guided by different points. In this example its guided by, max + min, zeros, and the inflection point.

diego_barcenas1 — 2021-02-01 21:22:23 UTC

I notice that there is a point of inflection, as well as a relative maximum and relative minimum. I wonder why it says zeros on the derivative graph

sebastian_carranza — 2021-02-01 21:22:28 UTC

I notice that they mark 4 different points on the line.

andrea_ramirez32 — 2021-02-01 21:22:30 UTC

Notice: There are four important points in the sketch
Wonder: Is it an estimate or is it exact?

I notice there are 4 points on the graph. - Megha

2021-02-01 21:22:34 UTC

Jasmine

2021-02-01 21:22:38 UTC

I notice that there's a maximum and minimum point.

jennifer_macy — 2021-02-01 21:22:41 UTC

I notice that there are minimum and maximum points on a curve sketch, along with zeros and inflection points.

jose_romero16 — 2021-02-01 21:22:50 UTC

I notice that it has a couple of points consisting of zeros, local max, and min points, and an inflection point. I'm wondering what local means.

chloeannemhari_reyes — 2021-02-01 21:22:55 UTC

I wonder what "local" means?

elyna_dotimas — 2021-02-01 21:22:59 UTC

Notice: max- highest point
min- lowest point
zeros refers to points when y is 0

Wonder: how do we know the exact points of inflection or is it just an estimate?

sruthy_sabesan — 2021-02-01 21:23:02 UTC

Maxima and Minima:
A local maximum point on a function is a point (x, y) on the graph of the function
whose y coordinate is larger than all other y coordinates.
A local minimum
point if it has locally the smallest y coordinate
Inflection Point:
Where the curve of the graph goes from concave down to up or vice versa. When the slope is 0 the concavity doesn't change.

Gabby A.

2021-02-01 21:23:12 UTC

I notice that the local max is on (0,0). The inflection point is half way between the local max and local min.

Guadalupe B

guadalupe_baltazar — 2021-02-01 21:23:16 UTC

I noticed that there are minimum/maximum points in the sketch.

tehzeeb_siddiqui — 2021-02-01 21:23:35 UTC

I notice the inflection point, which is the point where the concavity of the graph changes. I wonder what it means when it says "local" max or min.

prinay_singh — 2021-02-01 21:24:21 UTC

Prinay- I noticed that one point has a max and one point has a min on the graph.

jannelle_aquino — 2021-02-01 21:25:03 UTC

I notice that on a curve stretch, 4 points labeled on the graph are the max and min, zeros, and inflection points.

kiane_souvannavong — 2021-02-01 21:25:43 UTC

I notice on the sketch, 4 points labelled there is maximum, minimum, the zero and the inflection point.

andrea_ramirez32 — 2021-02-01 21:38:27 UTC

It would be more helpful since you would have less numbers to worry about.

sruthy_sabesan — 2021-02-01 21:38:37 UTC

The second derivative determines the rate of the first derivative which will help accurately graph the derivative function.

diego_barcenas1 — 2021-02-01 21:38:43 UTC

Knowing the second derivative might be helpful in graphing the original function because it tells you the location of the maxima and minima, and you can work backwards to come up with the original function.

elyna_dotimas — 2021-02-01 21:38:44 UTC

Knowing f"(x) might be helpful in graphing the key features of the original function such as the point of inflection (where slope curves).

ashley_laraharo — 2021-02-01 21:38:46 UTC

It can be helpful because the 2nd derivative gives you the rate of the derivative function which then connects back to the original function.

Guadalupe Baltazar

guadalupe_baltazar — 2021-02-01 21:38:50 UTC

Knowing f''(x) can be helpful in graphing the key features of the original function because it will give us an easier way to find the maxima/ minima.

Megha Jaswal

2021-02-01 21:38:56 UTC

It would be helpful to find the rate of the original function.

sebastian_carranza — 2021-02-01 21:39:00 UTC

It would be helpful because it gives you more information on the base function.

Jasmine

2021-02-01 21:39:05 UTC

It can be helpful because it can help you determine where the maxima and minima are.

dena_meseret — 2021-02-01 21:39:13 UTC

It might be helpful because we could find the minima and maxima

jennifer_macy — 2021-02-01 21:39:16 UTC

It might be helpful knowing f"(x) because it will help you with plotting points like the inflection point on the graph.

jose_romero16 — 2021-02-01 21:39:18 UTC

Knowing f''(x) might be helpful because it tells you where the maxima and minima is located.

Gabby A

2021-02-01 21:39:36 UTC

knowing the function would be helpful because it shows you the maximum and minimum, so you can work from those to get the rest of the function

chloeannemhari_reyes — 2021-02-01 21:39:51 UTC

Knowing f"(x) might be helpful when graphing the key features of the original function like the point of inflection.

tehzeeb_siddiqui — 2021-02-01 21:40:11 UTC

It's helpful to know f''(x) because it might help you figure out where the important points are, like the inflection point or the max and min.

kiane_souvannavong — 2021-02-01 21:40:21 UTC

knowing f(x) can help identify the important features in the function, specifically the maximum and minimum.

jannelle_aquino — 2021-02-01 21:41:27 UTC

it would be more helpful because it narrows down to the rate of the derivative that connects to the original function

prinay_singh — 2021-02-01 21:42:56 UTC

Prinay-Knowing f”(x) can help you find the rate of the function and can help you find where the max and min are located in the graph.

brenda_morales — 2021-02-01 23:56:01 UTC

I would probably want to focus on making sure I understand any concepts taught and the problems themselves so I have the ability to fully justify and defend my answers/solutions.

brenda_morales — 2021-02-02 00:28:29 UTC

I noticed that the sketch shows the ithe graphs zeroes, local max and min and the inflection point. I wonder why it is specifically called the "local" max and min

brenda_morales — 2021-02-02 02:44:50 UTC

f''(x) can be helpful in graphing key features as it simplifies the graph down and helps you find the rate of change of the original function

It is helpful to know the second derivative of a function because it assists us in finding the point of inflection as well as the maxima and minima. -Felipe

2021-02-02 17:31:33 UTC

I notice two points of zero, a maxima and a minima, and a point of inflection of a function.

felipe_delgado — 2021-02-02 17:35:58 UTC

Wonder: How do we determine the point of inflection?

I will focus on taking notes, studying the correct way, and stay focused in lecture. A challenge would be stay 100% focused as there are distractions. No questions.

felipe_delgado — 2021-02-02 17:37:33 UTC

jcho11 — 2021-02-03 04:35:01 UTC

Critical points are in relation to the derivative and based on the picture it seems like it is used to estimate or identify a minima and maxima of a function. -Felipe Delgado

2021-02-03 19:18:09 UTC

Critical points can give us the local minima and maxima of a function. -Felipe Delgado

2021-02-03 19:19:45 UTC

sruthy_sabesan — 2021-02-03 19:21:13 UTC

Critical points and significance:
- when derivative is 0 or unknown determines extremum (horizontal slope) and whether or not they exist
- the x-coordinate(s) of the min and max points determines x-intercept(s) of the derivative function

andrea_ramirez32 — 2021-02-03 19:23:55 UTC

Critical points can tell us what the max and min are

ashley_laraharo — 2021-02-03 19:24:01 UTC

Critical points tell us the max or min of a function's graph.

The challenging part was figuring out what to annotate. I don't really like doing all the extra stuff besides highlighting, it gets confusing and messy for me. Finding the critical points and how to calculate in order to get them looks like a simple process and is clear and makes sense to me. Does it get more complex with different functions or is it the same steps no matter what type of functions you work with? - Felipe Delgado

2021-02-03 19:26:15 UTC

ashley_laraharo — 2021-02-03 19:26:41 UTC

Critical points are when the derivative is 0 or undefined, and they help estimate if a function has a maximum or minima, but the points are not guaranteed.

Jasmine

2021-02-03 19:27:30 UTC

Critical points can tell us where the maxima and minima are.

sruthy_sabesan — 2021-02-03 19:27:55 UTC

In the last step of the process, where there are quadratic functions or polynomials as answers in some cases it may be difficult to solve for x-value(s). Everything else is crystal clear! No questions!

diego_barcenas1 — 2021-02-03 19:28:14 UTC

Critical points give us the information about where the minima and the maxima is.

Jasmine

2021-02-03 19:28:29 UTC

Critical points are when the derivative is 0 or undefined. They can help us find the maxima or minima.

andrea_ramirez32 — 2021-02-03 19:29:00 UTC

The most challenging part was figuring out what it meant when it said to plug in all three of the values into the original function but once I did figure that out, it was very clear.

tehzeeb_siddiqui — 2021-02-03 19:29:17 UTC

Critical points tell us where the maxima and minima are.

diego_barcenas1 — 2021-02-03 19:29:25 UTC

When critical points are derived, they become the zeros of the function. If we work backwards, they give us an idea where the critical points are.

Megha

2021-02-03 19:29:30 UTC

- Does not guarantee a maxima or minima
- Points where derivatives is zero or undefined

Hailee Cazatt

hailee_ballardocazatt — 2021-02-03 19:29:59 UTC

Critical points can tell us what the max and min points are

diego_barcenas1 — 2021-02-03 19:30:22 UTC

Everything seems straight and clear. However, a challenging step of the process is finding when you are going from the derivative function to the previous function. You have to find the y value of the zero, and work with polynomials to solve it.

jose_romero16 — 2021-02-03 19:30:29 UTC

It gives us the information of where the maxima and minima are.

elyna_dotimas — 2021-02-03 19:31:22 UTC

Critical points show the local max and min. (hills and valleys)

jose_romero16 — 2021-02-03 19:31:31 UTC

Critical points are when the derivative is 0. They help find the maxima and minima, although it's not always the case.

chloeannemhari_reyes — 2021-02-03 19:32:26 UTC

Critical points show the local max and min.

Hailee Cazatt

hailee_ballardocazatt — 2021-02-03 19:32:42 UTC

Critical points are where zero or unknown is the derivative. This points are crucial to describe since they are used to assess whether or not we have a function's local maximum or local minimum.

Megha

2021-02-03 19:32:56 UTC

What does a local maxima and local minima means?

chloeannemhari_reyes — 2021-02-03 19:33:05 UTC

Critical points are when the derivative is 0 or undefined. They are used to determine whether or not there is a local max and min of a function.

Jasmine

2021-02-03 19:33:11 UTC

The challenging part was what it meant when it said "local" for the maxima and minima.

elyna_dotimas — 2021-02-03 19:33:25 UTC

Critical points help us determine if there is a max and min of the function and if so, where they lie on the graph. They also let us know where the derivative is = 0 or undefined.

andrea_ramirez32 — 2021-02-03 19:33:52 UTC

Critical points are when the derivative is zero or undefined and can sometimes help us figure out what the max and min of a function is.

Guadalupe Baltazar

guadalupe_baltazar — 2021-02-03 19:34:00 UTC

- Something we can get from this is the way how critical points can change.
- Critical points helps us identify the maxima and minima on a graph.

ashley_laraharo — 2021-02-03 19:34:25 UTC

Personally, I didn't struggle with the process because the lesson is clear and easy to annotate. I was able to understand what critical points are and how to solve them.

Guadalupe Baltazar

guadalupe_baltazar — 2021-02-03 19:34:43 UTC

- Critical Points are when the derivative is 0 or undefined.
- They help us by determining if the function we have a local maxima/minima.

Megha

2021-02-03 19:35:06 UTC

- Critical points tells us the local max and local min.

jose_romero16 — 2021-02-03 19:35:47 UTC

I didn't have much trouble with the process and everything was rather clear. When factoring down you might get some weird numbers or quadratics which might make it a bit confusing depending on it.

Hailee Cazatt

hailee_ballardocazatt — 2021-02-03 19:35:53 UTC

Apart from highlighting and commenting for questions or clarification, I don't really like doing all the extra things, it gets overwhelming and I feel it is messy. When it said "local" for maximum and minimum I got a bit confused. And I think I have a basic understanding of how to find the critical points

Guadalupe Baltazar

guadalupe_baltazar — 2021-02-03 19:36:22 UTC

The challenging part was figuring out how to plug the x values back into the original function. Looking at the steps, I think I get an idea. Other than that, I have no other challenges.

tehzeeb_siddiqui — 2021-02-03 19:37:52 UTC

Critical points are when the derivative is zero or undefined. They can help us determine whether there's a local maxima or minima of the function.

chloeannemhari_reyes — 2021-02-03 19:38:16 UTC

Overall the process is clear. I may struggle when it comes to factoring because I can be slow. I don't have questions.

jennifer_macy — 2021-02-03 19:42:37 UTC

Critical points can show use the maxima and minima on a graph

tehzeeb_siddiqui — 2021-02-03 19:42:43 UTC

I understand most of the process since the steps are pretty straight forward. However, I was a little confused about the part where you factor the function and solve for all x solutions, but maybe I'll understand it better if I look at more examples? I also still don't know what local max and min means.

elyna_dotimas — 2021-02-03 19:45:16 UTC

It makes sense but there's factoring so I need to review that.

jennifer_macy — 2021-02-03 19:52:07 UTC

Critical points are are when the derivative is 0 or undefined. They can help us locate the maxima or minima of a function.

2021-02-03 19:56:21 UTC

maximum and minimum points, also they are points where the slope is zero.

The minima and maxima point

dena_meseret — 2021-02-03 20:02:19 UTC

dena_meseret — 2021-02-03 20:24:14 UTC

Critical points are the coordinates of a derivative when it equals 0

dena_meseret — 2021-02-03 20:26:35 UTC

Everything was pretty easy for me, but the logistics behind the steps were confusing.

jennifer_macy — 2021-02-03 20:33:17 UTC

I didn't have much trouble processing anything, so far it seems pretty straight up, but if I do have questions as I go along or am confused I'll me sure to check in

sebastian_carranza — 2021-02-03 22:36:37 UTC

Critical points are the maximum and minimum points.

sebastian_carranza — 2021-02-03 22:40:33 UTC

Critical points are when the derivative is 0 or undefined. They help us find whether there is a maxima or minima point on a function.

sebastian_carranza — 2021-02-03 23:36:23 UTC

Everything makes sense, it'll just take a few tries to fully get it.

Prinay

prinay_singh — 2021-02-04 01:51:58 UTC

Critical points can help us where are the max and min values are at on a graph.

Prinay

prinay_singh — 2021-02-04 01:54:06 UTC

Critical points are when the derivative is either undefined or zero but they can help us the max and min values of the function.

Prinay

prinay_singh — 2021-02-04 01:59:08 UTC

The part of the process that was challenging was figuring out how to solve the 2nd Derivative, 3rd Derivative, 4th Derivative, and 5th Derivative. The part of the process that was clear was annotating the slides. I have no questions.

andrea_ramirez32 — 2021-02-04 19:51:17 UTC

We can find and test the critical points by using the first derivative of a function.

dena_meseret — 2021-02-04 19:51:22 UTC

You can test whether a critical point is at its minima or maxima thought the 1st derivative test.

elyna_dotimas — 2021-02-04 19:51:29 UTC

Critical points can tell us the max or min but we have to use the first derivative test to know which one it is. If there is more than one critical point do you test all three?

Megha Jaswal

2021-02-04 19:51:31 UTC

We can find critical points using the function and we can find the if it local maxima or local minima by testing it.

diego_barcenas1 — 2021-02-04 19:51:38 UTC

Critical points can tell us where the maximum and minimum of a function are going to be by using the derivative test. A question I have is if there is a easier way to factor out the greatest common denominator of the first derivative.

Critical points are test points and not for sure when deciding the local minima and maxima. The first derivative test needs to be used to determine that. Is their a simpler process for the first derivative test? -Felipe Delgado

2021-02-04 19:51:41 UTC

ashley_laraharo — 2021-02-04 19:51:46 UTC

Critical points can be tested by using a sign chart. I don't have ?'s.

Jasmine

2021-02-04 19:51:46 UTC

Critical points help us find the maxima or minima of a point. I don't really have any questions.

chloeannemhari_reyes — 2021-02-04 19:51:49 UTC

Critical points tell us the local max or min. I don't have any questions!

jose_romero16 — 2021-02-04 19:51:54 UTC

Critical points can tell us the max and min by using a point to the left and right of it.

brenda_morales — 2021-02-04 19:52:01 UTC

One thing I learned about critical points is that you can find a functions critical points by first finding the derivative of the original function and then set the derivative equal to 0 and solve for x.

tehzeeb_siddiqui — 2021-02-04 19:52:13 UTC

Critical points tell us where the maxima and minima are but they don't tell us which point is a maxima and which is a minima so you have to test it yourself.

Ryan T

2021-02-04 19:52:28 UTC

The maximum and minimum points on a graph, where the slope is zero.

sruthy_sabesan — 2021-02-04 19:52:28 UTC

I know that you can use the first derivative test to figure out if our critical point is a local max or min. No questions!

Sebastian Carranza

2021-02-04 19:52:28 UTC

You need to find the first derivative of the function and equal it to zero to find the points.

Gabby Anderson

2021-02-04 19:52:35 UTC

critical points can be derived from factoring the first derivative

I

2021-02-04 19:53:00 UTC

Guadalupe Baltazar

guadalupe_baltazar — 2021-02-04 19:53:02 UTC

Critical points helps us identify if we have a local maxima/minima of a function. We can test the critical points by using the 1st derivative of a function.

kiane_souvannavong — 2021-02-04 19:53:16 UTC

critical points tell us where the max and min are. But we must test it to determine which is which basically (max and min)

prinay_singh — 2021-02-04 19:53:52 UTC

Prinay- You can find critical points by solving a function which is what I learned about today in this class.

Gabby A.

2021-02-04 19:55:23 UTC

I understood most everything about the process. The way to really ingrain it into my brain would be to continue to practice it. The challenging part was wrapping my brain around how to do the first derivative, then the rest made more sense.

Gabby A.

2021-02-04 19:57:52 UTC

Critical points are where the function levels off, whether that be max or min. In other words, its where the derivative equals 0.

Gabby A.

2021-02-04 19:59:38 UTC

These critical points tell us the max and min of the graph.

jennifer_macy — 2021-02-04 21:21:33 UTC

Critical points can help us determine the max and min but you need to do the first derivative test to check first.

brenda_morales — 2021-02-05 03:20:42 UTC

Critical points show us the max and the min of the function

brenda_morales — 2021-02-05 03:36:19 UTC

Critical points are when the derivative is either equal to 0 or is undefined. These points can help us determine the local min and max

brenda_morales — 2021-02-05 03:37:25 UTC

I find most of the process to be clear and generally easy to understand although I tend to struggle with factoring so that can be a challenge for me when finding critical points.

kiane_souvannavong — 2021-02-05 20:25:34 UTC

Learning about it was a breeze, the steps were easy to look over. At first it can be confusing so the only challenging thing I'd have to worry about the end results and seeing if they become weird numbers.

kiane_souvannavong — 2021-02-05 20:56:24 UTC

Critical point: the derivative is undefined or zero. Helps find maximum and minimum values on the functions. When we test it out, it helps us determine if its whether minimum or maximum.

kiane_souvannavong — 2021-02-06 22:45:28 UTC

Critical points can determine the local minimum value along with finding the maximum on a function.

jcho11 — 2021-02-08 15:42:14 UTC

jcho11 — 2021-02-08 15:44:45 UTC

jcho11 — 2021-02-08 15:44:52 UTC

jcho11 — 2021-02-08 15:45:00 UTC

jcho11 — 2021-02-08 15:45:17 UTC

jcho11 — 2021-02-08 15:45:27 UTC

diego_barcenas1 — 2021-02-08 21:20:21 UTC

The first derivative test is used for finding out the minimum and maximums of a function. It also allows you to find out the direction between specific intervals the graph is going in.

elyna_dotimas — 2021-02-08 21:20:30 UTC

The first derivative test is used to determine if there is extrema at the critical points.

jose_romero16 — 2021-02-08 21:20:37 UTC

The first derivative test is used to find the minimum and maximums by telling us if a value is positive or negative.

jennifer_macy — 2021-02-08 21:20:40 UTC

The first derivative test is used to find the positive and negative slopes --> the local max and min

Jasmine

2021-02-08 21:20:41 UTC

The first derivative test is used to find the maxima or minima.

2021-02-08 21:20:41 UTC

The first derivative test is used to find the local maxima and minima of the critical points. - Megha

dena_meseret — 2021-02-08 21:20:42 UTC

The 1st derivative test is used to help you figure out if the critical points are minima or maxima points.

Ryan T

2021-02-08 21:20:45 UTC

The first derivative test is used to find the min and max of the function

sebastian_carranza — 2021-02-08 21:20:46 UTC

The first test is used for finding the maximum and minimum points.

ashley_laraharo — 2021-02-08 21:20:52 UTC

The first derivative test is used to test critical numbers to see whether they have a local min or max.

Guadalupe Baltazar

guadalupe_baltazar — 2021-02-08 21:20:54 UTC

The first derivative test is used to determine the local minimum/maximum of a function.

chloeannemhari_reyes — 2021-02-08 21:20:55 UTC

The first derivative test is used to find the local max and min.

brenda_morales — 2021-02-08 21:21:00 UTC

The first derivative test is used to determine if the function has a relative maximum or minimum and also gives us information on the slope of the graph

gabby a

2021-02-08 21:21:08 UTC

the first derivative is to find the critical points / the maximum and minimum

andrea_ramirez32 — 2021-02-08 21:21:10 UTC

The first derivative test let's you figure out the max and min using the critical points.

sruthy_sabesan — 2021-02-08 21:21:22 UTC

The first derivative test is used determine whether extremum points exist and if so determine as increasing (positive) or decreasing (negative) slopes.

tehzeeb_siddiqui — 2021-02-08 21:21:31 UTC

The first derivative is used to figure out which critical points are maxima or minima.

jannelle_aquino — 2021-02-08 21:21:44 UTC

The first derivative is used to find the maximum and minimum points

2021-02-08 21:22:07 UTC

The first derivative test is used to determine if a function's graph has a local minima or maxima at a certain point and in which direction it is moving. -Felipe D.

prinay_singh — 2021-02-08 21:23:10 UTC

Prinay
The first derivative test is used for finding a local min and max points of the function.

Toys "R" US

2021-02-08 21:24:15 UTC

This toy store was flourishing in sales when it first started due to selling a variety of toys and more people buying toys in person. Currently the company filed for bankruptcy with more people shopping online, more competition, and more people buying electronics over toys. The inflection point would be right when Toys "R" US sales and etc. began decreasing.
-Felipe D.

2021-02-08 21:31:50 UTC

Red: Concave up
Blue: Concave down
Purple: Concave up
Orange: Concave down
-Felipe D.

diego_barcenas1 — 2021-02-08 21:31:54 UTC

The red is concave up because it goes from a sleep slope to a flat slope in the negative direction. The blue is concave down because it goes from step to flat. The purple is concave up, and the yellow is concave down

ashley_laraharo — 2021-02-08 21:32:05 UTC

Red = Concave up
Blue = Concave down
Purple = Concave up
Orange = Concave down

Jasmine

2021-02-08 21:32:08 UTC

Red: Concave up
Blue: Concave down
Purple: Concave up
Orange: Concave down

Guadalupe Baltazar

guadalupe_baltazar — 2021-02-08 21:32:09 UTC

Red = Concave up
Blue = Concave down
Purple = Concave up
Orange = Concave down

elyna_dotimas — 2021-02-08 21:32:18 UTC

Concave Up: purple, orange
Concave Down: Red, Blue

sebastian_carranza — 2021-02-08 21:32:19 UTC

Red is down, blue

jennifer_macy — 2021-02-08 21:32:23 UTC

Red: concave up
blue: concave down
purple: concave up
orange: concave down

jannelle_aquino — 2021-02-08 21:32:25 UTC

Red: concave down
Blue: concave up

brenda_morales — 2021-02-08 21:32:28 UTC

red = concave up
blue = concave down
purple = concave up
orange = concave down

2021-02-08 21:32:29 UTC

Red: Concave Up
Blue: Concave down
Purple: Concave up
Orange : concave Down
- Megha

dena_meseret — 2021-02-08 21:32:37 UTC

Red = Concave up Blue= Concave down
Purple= Concave Up
Orange = Concave down

chloeannemhari_reyes — 2021-02-08 21:32:44 UTC

red: concave up
blue: concave down
purple: concave up
orange: concave down

sruthy_sabesan — 2021-02-08 21:32:47 UTC

Red = Concave Up
Blue = Concave Down
Purple = Concave Up
Orange = Concave Down

jose_romero16 — 2021-02-08 21:32:58 UTC

Red: Concave Up
Blue: Concave Down
Purple: Concave Up
Orange: Concave Down

gabby a

2021-02-08 21:32:59 UTC

red : concave up
blue : concave down
purple : concave up
orange : concave down

tehzeeb_siddiqui — 2021-02-08 21:33:10 UTC

red: concave up
blue: concave down
purple: concave up
orange: concave down

andrea_ramirez32 — 2021-02-08 21:33:20 UTC

red=concave up
blue=concave down
purple=concave up
orange= concave down

2021-02-08 21:35:16 UTC

red concave up
blue concave down
purple concave up
orange concave down

prinay_singh — 2021-02-08 21:35:53 UTC

Prinay
Red- Concave up
Blue- Concave Down
Purple- Concave Up
Orange- Concave Down

diego_barcenas1 — 2021-02-08 21:47:01 UTC

A company that has faced an inflection point is chuck e cheese. Chuck E Cheese was very popular because of its arcade approach and idea. But, as video games came around and poor decisions, their sales went down, especially after saving their competitor. However, Chuck E Cheese reinvented itself, and turned a positive inflection point, with birthday parties and large fundraisers. However, due to 2010's people didn't go out as much, and you could download arcade games. Also, Shane Dawson started a conspiracy theory that Chuck E Cheese recycled pizza which hurt them significantly.

dena_meseret — 2021-02-08 21:47:16 UTC

I was also thinking about Toys R Us

ashley_laraharo — 2021-02-08 21:47:16 UTC

I have had an inflection point in my life.

Guadalupe Baltazar

guadalupe_baltazar — 2021-02-08 21:47:30 UTC

- A company that has faced an inflection point would be Payless since people started to lose interest (lack of sales since there was a lot of competition) and the company didn't pace themselves on spreading stores around which led them to go bankrupt.

Ryan T

2021-02-08 21:47:39 UTC

I haven't really had an inflection point in my life but I think that the college I chose will be an inflection point

sebastian_carranza — 2021-02-08 21:47:43 UTC

Blockbuster had an inflection. The rise of streaming took it over.

chloeannemhari_reyes — 2021-02-08 21:47:52 UTC

My inflection point would be choosing to go to Impact or another school.

Jasmine

2021-02-08 21:47:56 UTC

Blockbuster was a company that had an inflection.

elyna_dotimas — 2021-02-08 21:47:59 UTC

If I didn't go to Impact I would've gone to Mt. Eden and focused on orchestra.

jose_romero16 — 2021-02-08 21:48:11 UTC

Gamestop had quite a big inflection point where before it was the only place where you would usually buy games but as more retail stores started adding game sections and a lot of games being able to be bought digitally from the consoles and computers has stopped the incentive of buying from gamestop. Gamestop is still alive but it's on the verge of shutting down soon if things don't change.

sruthy_sabesan — 2021-02-08 21:48:17 UTC

Polaroid faced an inflection point as the basis for the instant camera was a chemical process that mimicked the darkroom, but when digital cameras flooded the market, Polaroid began losing some of its big customers in the real estate, insurance, and photo identification businesses.

jennifer_macy — 2021-02-08 21:48:18 UTC

An inflection point in my life would be deciding whether or not I would want stay homeschooling, or go to impact for middle school.

gabby a

2021-02-08 21:48:30 UTC

Sears isn't doing very well anymore. It used to be one of the biggest names in American retail, and is now barely hanging on. I'm not sure about everywhere, but at the local Southland mall all of the Sears buildings (auto center, appliance store, and retail building) have closed and are emptied out.

jannelle_aquino — 2021-02-08 21:49:09 UTC

an inflection point in my life was never signing to play for a volleyball club after trying out because i could’ve been scouted for colleges.

brenda_morales — 2021-02-08 21:49:12 UTC

I think that an inflection point in my life would be when my parents started letting me and my sister walk home alone as it was the first steps to my parents letting me be more independent.

Megha

2021-02-08 21:49:44 UTC

I think I had a inflection point in my life.

andrea_ramirez32 — 2021-02-08 21:50:04 UTC

Redbox is not doing so good since there are other platforms where you can watch movies

prinay_singh — 2021-02-08 21:50:10 UTC

Prinay
Chuck E Cheese and Toys R US did face an inflection and those two companies who owned these places went bankrupt.

tehzeeb_siddiqui — 2021-02-08 21:52:15 UTC

An inflection point in my life was when I chose to go to Impact for high school instead of Silver Oak.

hailee_ballardocazatt — 2021-02-09 07:17:53 UTC

The first derivative is used to find the maximum and minimum points

hailee_ballardocazatt — 2021-02-09 07:49:43 UTC

Red: Concave up
Blue: Concave down
Purple: Concave up
Orange: Concave down

dena_meseret — 2021-02-10 19:30:07 UTC

The 2nd derivative test seems to utilize steps of the 1st derivative test to complete it.

Megha Jaswal

2021-02-10 19:30:12 UTC

Similarities: the number line if find if it concave up or down.
Differences: Second derivative finds the inflection point and the first derivative tells the critical points.

chloeannemhari_reyes — 2021-02-10 19:30:33 UTC

A similarity I noticed between the first and second derivative test is that we set both derivatives to 0 then solve for x.

2021-02-10 19:30:34 UTC

Similarities: similar steps and process. Sign chart.

Differences: First Derivative test help to find critical points and second derivative test helps to find sub critical points and the point of inflection.
-Felipe Delgado

Jasmine

2021-02-10 19:30:40 UTC

Similarities: Number line, power rule
Differences: 1st derivative involves maxima/minima, 2nd derivative involves concave up/down

diego_barcenas1 — 2021-02-10 19:30:41 UTC

The similarities between the first and second derivative test is that the process is almost identical. You substitute a 0 for the y value, and work it from there to find the solutions and then you plug the values into the original equation. The differences are that in the first derivative test, you are finding a minimum/maximum while in the second derivative test, you are finding the concavity.

ashley_laraharo — 2021-02-10 19:30:44 UTC

In both tests you have to use the power rule to differentiate the original function. Also, we use the sign chart.

sebastian_carranza — 2021-02-10 19:30:45 UTC

A similarity between the two is that you set both to equal 0.

elyna_dotimas — 2021-02-10 19:30:46 UTC

Finding the sub-critical points is the exact same process of finding the critical points in the first derivative test.

Guadalupe Baltazar

guadalupe_baltazar — 2021-02-10 19:30:55 UTC

Similarities: In both the 1st and 2nd derivative test, we use a number line to identify if it concave up or down and set them both to equal zero.

tehzeeb_siddiqui — 2021-02-10 19:31:18 UTC

The difference is that first derivative test tells you about the slope and the local max and min, while the second derivative test tells you about the concavity and the inflection points. The similarity is that you use a sign chart for both.

Gabby A

2021-02-10 19:31:31 UTC

Similar : use the number line to determine if concave up or concave down; put both equal to 0

jennifer_macy — 2021-02-10 19:31:32 UTC

both test you need to use the power rule and both have similar processes.

brenda_morales — 2021-02-10 19:31:35 UTC

A similarity I noticed was that both the first and second derivative test you set the respective derivative to 0 and then solve for x and place the value(s) of x that you found in a sign chart. A difference is that the second derivative tells us the functions concavity and identifies inflection points while the first derivative gives us information on the slope and identifies local max and min

jose_romero16 — 2021-02-10 19:31:55 UTC

Similarities: Use the power rule, substitute for 0.
Differences: Use the first derivative test to find the critical points and the second derivative is used to find the concavity.

andrea_ramirez32 — 2021-02-10 19:31:59 UTC

In order to get the critical and sub critical points, you equal them to zero. The differences is that the second derivative only gives you sub-critical points, while the first derivative gives you critical points.

Ryan T

2021-02-10 19:32:14 UTC

For both tests you set the derivatives to 0, in the first test you find the critical points and the second test you find if the critical points are max or min

sruthy_sabesan — 2021-02-10 19:32:33 UTC

First derivative is the slope of the function, and the first derivative test is used to find the critical points, which are points where the derivative is equal to zero.
Second derivative is the concavity of a function, and the second derivative test is used to determine if the critical points (from the first derivative test) are a local max or min.

Prinay

prinay_singh — 2021-02-10 19:34:13 UTC

The similarities between the first derivative test and second derivative test are you have to use the power rule to find both of these derivatives and both can have concave up and concave down.

sruthy_sabesan — 2021-02-22 21:29:35 UTC

Optimizing path of travel (car, airplane, etc.) from point A to point B. Optimize deep learning neural network models (gradient descent) to effectively train a AI model for predicting house prices, image recognition, etc.

2021-02-22 21:29:36 UTC

Stretching : Maximize flexibility and minimize any tightness or risk of injury. -Felipe Delgado

diego_barcenas1 — 2021-02-22 21:29:36 UTC

When handling water distribution through pipes, you need to calculate the exact amount and rate water is being filtered. You might use optimization to make sure that the water is being filtered safely in the quickest rate possible

Hailee C

hailee_ballardocazatt — 2021-02-22 21:29:47 UTC

traveling by car

Jasmine

2021-02-22 21:29:49 UTC

Determining routes to different aircrafts

Guadalupe B.

guadalupe_baltazar — 2021-02-22 21:30:00 UTC

An example where we might use optimization would be traveling and using some sort of schedule.

ashley_laraharo — 2021-02-22 21:30:01 UTC

When practicing yoga we can maximize our strength, flexibility and mobility, and reduce/minimize sore inflexible muscles.

Jose Miguel

jose_romero16 — 2021-02-22 21:30:03 UTC

Optimizing things like underground fiber and the area it covers and where it's going to go would need a lot of optimization to get the best results.

E.D

2021-02-22 21:30:08 UTC

Optimization can be used to maximize profits and minimize production cost.

andrea_ramirez32 — 2021-02-22 21:30:16 UTC

You can use optimization on schedules in order to be more efficient

Megha

2021-02-22 21:30:18 UTC

Traveling

dena_meseret — 2021-02-22 21:30:24 UTC

When looking at different farming techniques. Are you focusing on maximizing the amount of produce, or the quality

Gabby A.

2021-02-22 21:30:35 UTC

when traveling, you would be trying to maximize the distance while also minimizing the cost

jannelle_aquino — 2021-02-22 21:30:35 UTC

An example would be profit in a business

brenda_morales — 2021-02-22 21:30:46 UTC

I think that in traveling optimization is used. If you're on the road you want to choose the fastest route to save time and gas. Then there's the concept of trying to do the most in a day.

jennifer_macy — 2021-02-22 21:30:56 UTC

When building you would use optimization to build efficiently - maximizing build time, but at a lower cost

prinay_singh — 2021-02-22 21:31:00 UTC

Prinay
A real world example of optimization is when any other transportation services optimize the schedule of the time.

Ryan T

2021-02-22 21:31:17 UTC

optimizing code for computers so that the program runs the fastest without using as much processing power

tehzeeb_siddiqui — 2021-02-22 21:32:03 UTC

It can be used for transportation, finding a way to get from one point to another, where the path is the shortest path you can take.

Armando Acosta

2021-02-22 21:32:25 UTC

Finding the right bus routes to take in order tho spend the least amount of money and time.

Chloe Anne Reyes

chloeannemhari_reyes — 2021-02-22 21:33:14 UTC

When shopping, maximize quality minimize price

diego_barcenas1 — 2021-02-22 21:54:08 UTC

I think what is confusing is maybe trying to see what the difference between maxing and minimizing will affect your equations and what you're solving. I understand the restraints based on the situation, but do we have to memorize any new formulas when forming the function with the independent variables.

ashley_laraharo — 2021-02-22 21:54:23 UTC

I am confused in the 3rd part of the problem where we have to reduce and substitute and then come up with inequality restrictions.

dena_meseret — 2021-02-22 21:54:24 UTC

I understand the substitution and how the questions are formed. The only confusing thing is the difference between constraints that are equal and unequal.

2021-02-22 21:54:26 UTC

The steps we went over make sense after being clarified especially by doing close reading as it helps me to understand better.
-Felipe Delgado

sruthy_sabesan — 2021-02-22 21:54:33 UTC

I understand how the optimization process works with 2D area and perimeter, however identifying inequality restrictions is definitely a growth area. The reason for each step is also unclear. I'm curious to learn about how it can be used with 3D figures.

Megha

2021-02-22 21:54:47 UTC

I am confused on the second step a little. I understand the third step on how to set the equation and the substitution.

elyna_dotimas — 2021-02-22 21:54:52 UTC

Why won't the regular area formula work? The math is understandable the why is confusing.

Do we have to remember geometry to do this?

Guadalupe Baltazar

guadalupe_baltazar — 2021-02-22 21:54:54 UTC

I understand what we have to do, but I'm a bit confused on step 3 (constraint).

jennifer_macy — 2021-02-22 21:54:57 UTC

I'm kind of just confused on it all in general. Well mostly kind of around steps 2 and 3, but kind of still confused altogether

Gabby A.

2021-02-22 21:55:00 UTC

its a bit confusing that we were talking about the area and plugging in the values for the area, and then started talking about the limitations again and doing more things with those.

jose_romero16 — 2021-02-22 21:55:32 UTC

I guess I would be confused for the maximizing and minimizing for the inequality.

brenda_morales — 2021-02-22 21:55:34 UTC

I think steps 2 and 3 can get a little confusing for me, more specifically the part were we solve for one constraint and then use substitution

Jasmine

2021-02-22 21:55:36 UTC

I am confused on the formula why we use that one.

tehzeeb_siddiqui — 2021-02-22 21:56:07 UTC

I'm kind of confused, like all the steps make sense and everything, but in general it's just kind of complex and I think if I look at more examples I'll understand it better.

andrea_ramirez32 — 2021-02-22 21:56:45 UTC

I'm just confused on the constraints . Like I understand what we have to do but how will we know when to use it? (if that makes sense??)

Chloe Anne Reyes

chloeannemhari_reyes — 2021-02-22 21:57:06 UTC

The math is clear. But similar to what Elyna said why can’t we use the original area formula.

Hailee C

hailee_ballardocazatt — 2021-02-22 21:57:27 UTC

The second part is a bit confusing but after re watching the video I am sure that could be fixed

prinay_singh — 2021-02-22 21:57:48 UTC

Prinay
What I understand are drawing a model to represent optimization and solving for one IV. I don’t understand how to use substitution to remove IV from the function and the constraints that are inequalities.

Armando

2021-02-22 22:00:03 UTC

The equality constraints are somewhat confusing, but everything else makes sense.

kiane_souvannavong — 2021-02-24 02:41:35 UTC

Blockbuster was an inflection, due to the fact that they are actually out of business and there are apps or places that you can stream movies from.

kiane_souvannavong — 2021-02-24 02:44:14 UTC

Red: concave up
Blue: concave down
purple: concave up
orange: concave down

kiane_souvannavong — 2021-02-24 02:44:53 UTC

First derivative is the test to find out the maximum and minimum points. which are maxima and minima.

kiane_souvannavong — 2021-02-24 02:52:34 UTC

Similarities: uses number line to determine if it concave up or down, (uses power rule) equals to zero.

Differences: first derivatives are for critical points, second derivatives are for concave.

diego_barcenas1 — 2021-02-24 19:51:53 UTC

First to optimize a function, what you have to to formulate the equation, as well as come up with constraints, as well as another function that represents the values you are working with. Then you want to work with the last iv, trying to find its value, and then plugging it back to the original function. After that, what you want to do is set the equation up as an inequality (x2), to find the last value, where there is zero. Then you want to find the first derivative and the second derivative, to find the critical points, the maxima and minima, and well as its concavity to find the maximum value. Then you want to plugin in the critical point to the original improved function to find the maximum value.

2021-02-24 20:41:24 UTC

Begin by drawing a model for reference. Then, create the objective function ( the A(x) one). Determine if you are trying to maximize or minimize. Determine the inequality constraints and then the equality constraint (perimeter). Solve for one independent variable (x or y). Use substitution in order to remove the independent variable from the objective function and inequality constraints. Find the critical points by using the first or second derivative test of the objective function. Determine if the critical point is a local maximum or minimum. Compare the endpoints in order to find the global extremum using the area function. Determine the maximum amount of space and the length and width. Lastly, confirm it using a graph of the area function.
- Felipe Delgado

chloeannemhari_reyes — 2021-02-25 19:41:27 UTC

1. Draw a picture and label with information you know.
2. Create equations with variables and consider constraints.
3. Reduce the number of variables and substitute into objective function and inequality constraints
4. Use power rule to find critical point
5. Use first or second derivative test to find local max and min.
6. Plug in critical point into objective function

1. Draw a picture, and define variables

dena_meseret — 2021-02-25 19:41:57 UTC

2. Formulate an equation with constraints
3. Solve the equation working with the independent variable.
4. Find the critical points by using the 1st and 2nd derivative test.
5. Using the critical points find the minimum and maximum
6. Then find the global extremum
7. Use a graph to check

ashley_laraharo — 2021-02-25 19:42:12 UTC

First, we draw the scenario for visualization. Then we create equations like the objective function, that relate to the variables and constraints. We then use the equality constraint to reduce and solve for one independent variable, and substitute it. Next we find the critical point of the objective function and test if they are local minimums or maximums. Finally we compare the objective function values at local extrema and at the endpoints to find the global extremum or "goal".

Megha Jaswal

2021-02-25 19:42:30 UTC

First, draw a model of the problem. Then, we have to formulate a equation A(x)- variable and constraints. Then, we solve the equation that we created. After than, find the critical points using the first derivative and second derivative test and find the sign chart to find out if it local maxima or minima. Finally, then plug in the maximum or minima in the equation to get the answer.

Jasmine

2021-02-25 19:52:00 UTC

First you draw a picture of the problem and label it. Then you create an equation with constraints and solve it. Next you find the critical points by using the 1st and 2nd derivatives. Finally you use those points to find either the maxima or minima.

andrea_ramirez32 — 2021-02-25 19:54:56 UTC

1) Draw a picture that's labeled with the information you are given
2) Create an equation that includes the variables and the constraints
3) Solve the equation so that you're left with less independent variables
4) Find the critical points by using the first derivative test or the second, if it calls for it
5) Plug in the critical points into the first or second derivative to figure out if the points are max or mins
6) Then find the global extremum by plugging in the critical points and/or endpoints

tehzeeb_siddiqui — 2021-02-25 19:58:47 UTC

First, draw a model for the scenario. Next, come up with an equation (in this case, for the area, so it would be A(x) = length x width). Write the constraints, to rule out the numbers that the length and width can't be, and to also include what values you already know (like the perimeter). Then, use the equality constraint to solve for one of the variables, and then using substitution, get rid of that variable so you're only left with one other variable in the equation, making it possible to solve. And then once you have the original equation (the A(x) one), but with only one variable instead of 2, take the derivative, find the critical point, and use a sign chart to figure out if that point is a local max or local min. Then, take that critical point and plug it into the area function to find out the global extrema. And then also check the end points (in this case, it's the points where the area would equal 0), to make sure those are the global max or min.

Guadalupe Baltazar

guadalupe_baltazar — 2021-02-25 20:05:59 UTC

1) We first draw a picture of the problem and label them.
2) We then create a formula/equation A(x)- variable and constraints and solve for it.
3)We look for the critical points by using derivatives and with a sign chart, we were able to identify if the point was local max or local min.
4) We plug in the local max/min in our area function to find the local extrema.

kiane_souvannavong — 2021-02-25 20:21:28 UTC

Step 2 and 3 are confusing steps to me. Setting up the equation is kinda hard and confusing to do but I guarantee if I work on it I"ll be able to get it.

kiane_souvannavong — 2021-02-25 20:29:57 UTC

Traveling Optimization can be used from finding one way to another and determining which path is the shortest to take.
Shopping can be used to maximize quality of the product is made from and minimizing the pricing.

kiane_souvannavong — 2021-02-25 20:41:04 UTC

1) Label and sketch your problem with the information given to you
2)formulate the A(x)- variable equation and solve for it.
3)Find critical points by using first and second derivative test, use sign chart (determine local min or local max).
4)plug in local max/min, to find final answer.

Prinay

prinay_singh — 2021-02-27 01:05:18 UTC

The first step for optimization produce is to draw visuals to represent the problem. The second step is to create an equation which is A(x) = x1 x2. The third step is to use the constraints to help you solve the equation. The fourth step is to find the critical points of the function. The fifth step is to use either the first derivative test or the second derivative test to help you find the max and min values of the function. The last step is to find the endpoints of the function to get your final answer of the optimization process.

jcho11 — 2021-03-01 02:14:25 UTC

jcho11 — 2021-03-01 02:14:58 UTC

Megha Jaswal

2021-03-01 21:18:42 UTC

Notice: Used the derivative to find the critical points and used the quadratic formula.
Wonder: why did you use the quadratic formula?

diego_barcenas1 — 2021-03-01 21:18:46 UTC

Notice:
- In the graph there is a function
- The derivative function is graphed
- I noticed the max/mins matched up with zeros
- x=100 was the point of inflection, it looks like
- Cho took the derivative and used the quadratic formula to find the zeros of the function
- He also did it another way; he used the line test to figure it out
Wonder:
- Did cho visually indicate in the graph where y = 14 (the minimum wage)

Jasmine

2021-03-01 21:19:10 UTC

Notice: Used 1st derivative and critical points
Wonder: Why was the quadratic formula used?

sruthy_sabesan — 2021-03-01 21:19:13 UTC

Notice
- found critical points to figure max which explores the possibility of a greater optimum wage that can employ more floor workers
- used quadrative formula b/c polynomial couldn't be factored
- used Desmos to cross reference

Wonder
- Why did you choose first derivative test over second derivative test when it's quicker?

Jose Miguel

jose_romero16 — 2021-03-01 21:19:18 UTC

I notice that the quadratic formula was being used. Critical points were used to find the max and min.

elyna_dotimas — 2021-03-01 21:19:25 UTC

I notice that Cho used desmos to graph the function & check his answers.

This looks more like the calculus we've been practicing.

andrea_ramirez32 — 2021-03-01 21:19:33 UTC

notice:
Although there were more steps involved, generally, the answer was the same as the one I got

wonder:
can there be more than one way to use optimization to figure out an answer?

Guadalupe Baltazar

guadalupe_baltazar — 2021-03-01 21:19:37 UTC

Notice:
- Used the first derivative to find critical points.
- Used the quadratic formula
- This has more steps but it leads us the same answer I have.

Wonder:
- How can we use optimization to figure out a problem like this?

brenda_morales — 2021-03-01 21:19:47 UTC

I noticed that the first steps taken were to find the critical points of the function and then use the first derivative test

ashley_laraharo — 2021-03-01 21:19:49 UTC

I notice that Cho found the critical points of the function to then see whether the maxima or minimum wage was the better choice.
Something I wondered before looking at this example was what were the endpoints, and in this case 14 was the endpoint.

dena_meseret — 2021-03-01 21:19:51 UTC

Notices: Finding critical points
Wonders:
Didn't know that we could say that the points are from Desmos.
When using the quadratic equation I couldn't find the critical points, was there a way to

jennifer_macy — 2021-03-01 21:20:10 UTC

I notice that the critical points were found of the function.

Gabby A.

2021-03-01 21:20:13 UTC

Notice : the derivative and critical points are used for this version
Wonder : is this method better or more correct than the other method shown?

chloeannemhari_reyes — 2021-03-01 21:20:19 UTC

I noticed Cho used the derivative and found the critical points.

I wonder how I can use your example to revise my summative.

2021-03-01 21:20:28 UTC

I noticed the usage of graphing functions. using the quadratic formula and applying that to formula provided in the assignment. I also noticed I got the same answer. I wonder what purpose the of the quadratic formula serves in this process of solving the question and why you decided to use it?
-Felipe Delgado

jannelle_aquino — 2021-03-01 21:21:12 UTC

I noticed that the quadratic formula was used

tehzeeb_siddiqui — 2021-03-01 21:21:42 UTC

I notice that I got the same answer by inputting w = 14 into the equation and then checking my work by graphing.

prinay_singh — 2021-03-01 21:22:31 UTC

Prinay
Notice: Using the quadratic formula for finding the critical points
Wonder: How will the second derivative test will play in this problem?

elyna_dotimas — 2021-03-01 21:48:08 UTC

1. model the scenario
2. create an equation that represents the situation (include constraints + variables).
3. use equality constraints to solve for one variable
4. find the critical points (where the derivative = 0)
5. use the first OR second derivative test to determine which extrema are local min/max (if they exist)
6. find global extremum

Jose Miguel

jose_romero16 — 2021-03-01 21:48:08 UTC

1. Draw a picture of the scenario
2. Create an equation that relate the variables and constraints.
3. Use equality constraints to solve for one variable.
4. Find the critical points (Where the derivative is 0)
5. Use the first or second derivative test find the local min and max
5. Find the global extremum.

sruthy_sabesan — 2021-03-01 21:48:36 UTC

1. Making an arbitrary guess of width and height of of 600 ft. of fencing.
2. Identify constraints and an area and perimeter formula to later interchange values through substitution.
A(x) = W x H
P = 2H + 3W = 600 ft.
W greater than(>) or equal(=) to 0
H greater than(>) or equal(=) 0
3. Using perimeter formula solved for the height in terms of the function.
H = 200 - (2/3)W
4. Plugged new found value H into the area formula identified earlier.
A(W) = W x ( 200 - (2/3)W)
= 200W - (2/3)W^2
W less than (<) 300ft.
5. Calculated derivative of current area function to maximize the width.
a. Solved for Critical Points
A'(W) = 200 - (4/3)W
= 150
b. Determined critical point was a local maxima
A'(100) = 200 - (4/3)(100)
= 66.66
A'(200) = 200 - (4/3)(200)
= -66.66
6. Solved original function for 150 to find the area and divided the area by the height to solve for the width.
7. The pen with the largest area would have a width of 100 feet, a length of 150 feet, and an area of 15,000 square feet.

jannelle_aquino — 2021-03-02 00:30:50 UTC

A similarity would be that they have the same step process and the first and second derivatives are solving for 0

jannelle_aquino — 2021-03-02 00:34:07 UTC

The points show maximum and minimum points of the function

jannelle_aquino — 2021-03-02 00:37:00 UTC

The critical points are when the derivative is undefined or 0. This will help find the minimum and maximum points.

jannelle_aquino — 2021-03-02 00:40:48 UTC

The steps are easy to understand and do but I just need to go over it a few times to get used to it.

chloeannemhari_reyes — 2021-04-29 18:41:48 UTC

Jennifer Macy

jennifer_macy — 2021-04-29 18:42:44 UTC

Question #3

sebastian_carranza — 2021-04-29 18:42:54 UTC

Diego Barcenas

diego_barcenas1 — 2021-04-29 18:42:54 UTC

ashley_laraharo — 2021-04-29 18:43:07 UTC

Felipe Delgado

2021-04-29 18:44:36 UTC

Megha Jaswal

2021-04-29 18:44:36 UTC

#5

elyna_dotimas — 2021-04-29 18:44:54 UTC

This was my attempt for #5. I wasn't sure how to integrate the e. Did anyone do anything different?

do we have to apply the antiderivative to the e too?

Guadalupe Baltazar

guadalupe_baltazar — 2021-04-29 18:45:26 UTC

Attempt For # 3

tehzeeb_siddiqui — 2021-04-29 18:46:59 UTC

dena_meseret — 2021-04-29 18:47:17 UTC

sruthy_sabesan — 2021-04-29 18:50:36 UTC

jose_romero16 — 2021-04-29 18:50:37 UTC

brenda_morales — 2021-04-29 18:52:55 UTC

Problem #2

Jasmine

2021-04-29 19:25:07 UTC

Problem # 2

2021-05-02 21:17:57 UTC

Prinay