Open Discussion by Jonathan Saputra

Hello!

joe_3a24 — 2019-04-03 08:26:26 UTC

This is just an example. You might also attach file or website to support your opinion and discussion.

Well...

joe_3a24 — 2019-04-03 08:27:58 UTC

You can also post more than one comment in here. Use English and appropriate language, okay?

Happy discussing!! :)

Max and Min Conditions of function of two/more variables by Agnes Ruth Ahimsa

araahimsa — 2019-04-04 17:44:51 UTC

In e-book I've read that the definitions is a function of two variables F(X,Y) has a ,local maximum at (a,b) if f(x,y) < f(a,b) for all points (x,y) in some disk with center (a,b). The value f(a,b) is called a local maximum of f.

And for the theorem :
If --> F is differentiable and has a local maximum or minimum s at (a,b)

Then --> Fx(a,b) =0 Fy 9a,b) = 0.

For the question example --> Find any local maximum&minimum of F(x,y) = x^2 - y^2!!

Maximum and Minimum Conditions of two variables by M. Alfin Prayogo

2019-04-05 02:48:20 UTC

A function ,f, of two variables is said to have a relative maximum or minimum at a point (a,b) if there is a disk centered at (a,b) , then f(a,b) ≥ f(x,y) (shows relative maximum), while f(a,b) ≤ f(x,y) (shows relative minimum) for all points (x,y) that lie inside in the disk.

a function ,f, is said to have an absolute maximum or minimum at (a,b) if f(a,b) ≥ f(x,y) (absolute maximum), while f(a,b) ≤ f(x,y) (absolute minimum)

"Maximum and Minimum Conditions" of Functions of Two (or more) Variables by Gemintang Bening Segara ASri

2019-04-05 22:11:11 UTC

From what I read, I got that;
when there is a factor with two or more variables with continuous second order partial derivatives fxx, fyy, fxy at a critical point (a,b) then:

D (a,b) = fxx(a,b) fyy(a,b) - [fxy(a,b)]^2

- If D > 0, and fxx(a,b) > 0, then f has a relative minimum at (a,b)
- If D > 0, and fxx (a,b) < 0, then f has relative maximum at (a,b)
- If D < 0, then f(x,y) has a saddle point at (a,b)
- If D = 0, the second derivative test is inconclusive.

For better understanding, check this video!

"Maximum and Minimum Conditions" of Functions of Two (or more) Variables - Shafira R. Khoirun Nisa

shafira_romadiana — 2019-04-06 14:16:51 UTC

In a single variable function, we use derivatives to find maximum and minimum. Similarly, in multivariate function, to find the maximum and minimum we also use derivatives, but it is a partial derivative.

A multivariate function centered at (a,b) has a local maximum at (a,b) if f(x,y) ≤ f(a,b) for all points (x,y) and the local minimum value is if the f(x,y) ≥ f(a,b) for all points (x,y).

There is also a theorem that tells about where we should look for maximums and minimums. If f is differentiable and has a local maximum or minimum at (a,b), then fx (a,b) = 0 and fy (a,b) = 0.

To determine the local maximum and minimum of a multivariate function, we also can use a second (mixed partial) derivative test. Here is the link for more explanation about second derivatives test:

Maximum and Minimum Condition of Function of Two Variable [Maulidina Lubis]

2019-04-06 16:52:53 UTC

In my understanding, a function of two variable has maximum at (a,b) if f(a,b) ≥ f(x,y). The maximum value of the function is f(a,b) and this occurs at (a,b). Global maximum is the highest point. However, f(a,b) ≤ f(x,y) (it is show that the function has minimum.

Finding maximum and minimum function. If the function define on open interval, and f(a,b) is a local extreme of f, then f'(a,b)=0

Please remind me if I have a misunderstanding

Maximum and Minimum Conditions of Function of Two or More Variable-fiella Pramysilia Citra

2019-04-06 17:05:17 UTC

The term of maximum, means the function's value is in the peak. While minimum condition shows that the function has the value in the bottom.

In order to determine whether a function's value is maximum or minimum, firstly, we suppose that:
The second partial derivatives continuous on a disk centered in f(a,b), then fx(a,b) and fy(a,b) are equal to 0.
Therefore,
D(a,b)=fxx(a,b)fyy(a,b)-fxy(a,b).
Results :
1. Minimum, whenever D>0 and fxx(a,b)>0.
2. Maximum, whenever D>0 and fxx(a,b)<0.
3. Saddle point, where D<0 and fxx(a,b) is neither maximum nor minimum.

For the better understanding, just check it out! :)
https://youtu.be/Hm5QnuDjNmY

Maximum and Minimum Condition of Function of Two Variable [Angelia Tarigan]

2019-04-06 17:43:25 UTC

Here I attach my opinion about maximum and minimum point of more than 1 variables based on the theory that I got from the E-book and a video from Youtube.
Click here to see the video :)

Maximum and Minimum Condition of Function of Two or More Variable [Anisa Pitriani K]

fitrianisakurahman_99 — 2019-04-07 10:53:54 UTC

Based on what I read on calulus 3 book, I got a definition:
"A function of two variables f(x,y) has a local maximum at (a,b) if f(x,y) ≤ f(a,b) for all points (x,y) in some disk with center (a,b). The value f(a,b) is called a local maximum value of f."

To determined the maximum and minimum value of two or more Variable, we can use a second (mixed partial) derivative, where :
fx(a,b) = 0 and fy(a,b) = 0
so, D(a,b) = fxx(a,b)fyy(a,b) – { fxy(a,b) }^2

1. If D > 0 and fxx(a,b) > 0, then f(a,b) is a local minimum.
2. If D > 0 and fxx(a,b) < 0, then f(a,b) is a local maximum.
3. If D < 0, then f(a,b) is a saddle point.)
4. If D = 0, then f(a,b) could be a local maximum or a local minimum or neither.

For the question example, click this video

Maximum and Minimum Condition of Function of Two or More Variables

charlinetiara — 2019-04-07 13:04:26 UTC

So, basically to determine whether a critical point was a local maximum or minimum using the second derivatives.

I've understand that the value f(a,b) is a local max. if f (x,y) ≤ f (a,b) for all points (x,y).

And there re four conditions that we must aware if we want to determine max. or min.

(i) If D > 0 and fxx (a,b) > 0, then f (a,b) is a local minimum.

(ii) If D > 0 and fxx (a,b) < 0, then f (a,b) is a local maximum.

(iii) If D < 0, then f (a,b) is not a local minimum or a local maximum. (It is a saddle point.)

(iv) If D = 0, then the test is "indeterminate": means it could be neither local max. nor local min.

In this case fxx and fyy will be the same because both of them are multiplication.

Faridah Tampubolon - Maximum and Minimum Conditions of Functions of two (or more) Variables

2019-04-07 13:11:56 UTC

This is using second derivative test. Suppose that the second partial derivatives of F are continuous, with center (a,b) and suppose that fx(a,b)=0 and fy(a,b)=0.
The formula is D= D(a,b)= fxx(a,b)fyy(a,b)- fxy(a,b).
This of maximum o minimum point can be defined in to 4 conditions such as;
1. if D>0 and fxx(a,b) >0, then f(a,b) is a local minimum
2. if D>0, fxx(a,b)<0, then f(a,b) is a local maximum.
3. if D<0, then f(a,b) is not a local max/min
4. If D = 0, then the test is "indeterminate": f(a,b) could be a local max/min or neither.

Here I attached the example of "Find local max, local min, saddle points"

Krishna Dharma [Max and Min Conditions of Multivariable functions}

2019-04-07 16:10:20 UTC

It is basically similar to what was learnt in Calculus 1, however this time we will be dealing with two or more variables. The concept is still the same which is finding the relative max or min points by finding out their partial differentials fx and fy. A critical point of a multivariable function is a point where the partial derivatives of first order of this function are equal to zero. We can use it to determine whether the point is a local maximum or a local minimum.

"maximum and minimum conditions" of functions of two (or more) variables?

irmalasari531 — 2019-04-07 19:08:56 UTC

I agree with Krishna. this is similar with calculus 1. but differences with calculus 1 and 3 is variables. if I not mistaken in calculus 1 we just learn in Maximum and minimum condition in one variable and then how if the variable more than one. According the research that I can find maximum and minimum in two variablels or more in can be happen. for example f(x) = x^3 - 4x^2 + 5x + 2 when f'(x) = 0 . it can see in the link that I'am given. the concept same with one variables but in one variable just oce differential in the two or more variable have twice differential.
This is that I get from that link. if I'm mistaken understand. let me know. someone can add comment in my opinion. it is my plesure if you add the comment for me. Thank you.

Maximum and Minimum Condition of function in two or more variable-Dilla Ayu Wardani

2019-04-08 00:30:38 UTC

According to E-book Calculus III that I read, local maximum and minimum in two or more variables can be determined by finding second (mixed partial) derivative test. Local maximum in two or more variables (a,b) is defined if f(x,y) ≤ f(a,b) for all points (x,y) in some center disk (a,b). In addition, if the function is differentiable and has local maxima or minima in (a,b), so the f_x (a,b) and f_y (a,b) equal to zero.

Second derivative test is used to determine whether the function is local maxima, local minima or the saddle point.

Here is the rule for second derivative test:

If we have fxx , fxy , fyx , and fyy are continuous in a disk with center (a,b) and f_x(a,b) = 0 and f_y(a,b) = 0. Let D = D(a,b) = f_xx(a,b)f_yy(a,b) – { f_xy(a,b) }

(i) If D > 0 and fxx(a,b) > 0, then f(a,b) is a local minimum.

(ii) (ii) If D > 0 and fxx(a,b) < 0, then f(a,b) is a local maximum.

(iii) (iii) If D < 0, then f(a,b) is nor in a local minimum or a local maximum. (It is a saddle point.)

(iv) (iv) If D = 0, then the test is "indeterminate": f(a,b) could be a local maximum or a local

minima or neither.

Maximum and Minimum Condition of Function in Two or More Variable (Nur Fatikhah)

nurfatikhah99 — 2019-04-08 02:34:26 UTC

Based on Calculus 3 E-book
To determining the maximum or minimum of function we must to know encountered in geometry, mechanics, physics, and other fields, and was one of the motivating factors in the development of the calculus
This is the same with the materials of Calculus 1.

In Maximum and Minimum Condition we will learn about The Second Derivative.

The Second Derivative is employed to determine if a critical point is a relative maximum or relative minimum.

f''(x_c)>0, then x_c is a relative minimum.
f''(x_c)<0, then x_c is a relative maximum .
The notions of Critical points and the second derivative is over to function of two variables (Let z=f(x,y))

For The Second Derivative Test for Function of Two Variable.

Let (x_c, y_c) be a critical point.
We have the following cases:

If D>0 and f_xx(x_c,y_c)<0, then f(x,y) has a relative maximum at (x_c,y_c).
If D>0 and f_xx(x_c,y_c)>0, then f(x,y) has a relative minimum at (x_c,y_c).
If D<0, then f(x,y) has a saddle point at (x_c,y_c).
If D=0, the second derivative test is inconclusive.

Maximum and Minimum in Bounded Region
- Has three types of points that can potentially to be maximum or minimum

Relative extrema in the interior of the square.
Relative extrema on the boundary of the square.
Corner Points.

Maximum and Minimum Conditions of Function in Two or More Variable

filiniagusti12345 — 2019-04-08 03:28:09 UTC

based on book Calculus 3 tell me that use second derivatives to determine either the maximum or minimum of some f (function).
We can use the Formula of second derivatives where fx(a,b) = 0 and fy(a,b) = 0

so, D(a,b) = fxx(a,b)fyy(a,b) – { fxy(a,b) }^2

I believe all of you know it well if Local maximum at (a,b) if f (x,y) ≤ f (a,b) for all points

(x,y) with center (a,b). Also for the feature materials can we get form the class and book.

We need to learn this condition to understand the function either max or min.

Maximum and minimum conditions of functions of two or more variables

kristiansolemankuli — 2019-04-08 03:38:43 UTC

[Kistian Soleman Kuli]

To find the local maximum and
local minimum in two or more variables we have to solve the partial derivative.
At two variable and centered at disk (a,b), then the local maximum at (a,b) if f(x,y) ≤ f(a,b) and local minimum f(a,b) ≤ f(x,y) for all point (x,y)
with the equation
D(a,b) = fxx(a,b)fyy(a,b) – { fxy(a,b) }^2

If the critical point can not determine maximum and minimum, then it is a saddle point (showed on the picture).

Understanding Maximum and Minimum Condition of a Function (Part 1)

jeanyovini1106 — 2019-04-08 04:14:10 UTC

Hey guys! Since everyone has shared the ideas of finding the minimum and maximum conditions of two variable, I will try to explain it very quickly and in a fun way! Also you can check out more about the detail in the link down below :
https://www.mathsisfun.com/calculus/maxima-minima.html

Finding Maxima and Minima using Derivatives

Where is a function at a high or low point? Calculus can help!

A maximum is a high point and a minimum is a low point. In a smoothly changing function a maximum or minimum is always where the function flattens out (except for a saddle point).

Where does it flatten out? Where the slope is zero.

Where is the slope zero? The Derivative tells us!

Second Derivative Test

When a function's slope is zero at x, and the second derivative at x is:

less than 0, it is a local maximum
greater than 0, it is a local minimum
equal to 0, then the test fails (there may be other ways of finding out though)

Maximum and minimum conditions

taradf46 — 2019-04-08 04:28:11 UTC

The thing that I know from maximum and minimum is the way to find it.
Second derivative of a function will determine the maximum and minimum.
I suggest you guys to open this link http://hyperphysics.phy-astr.gsu.edu/hbase/Math/maxmin.html. It helps you to understand by stated the example of maximum and minimum calculation.

In calculus, the maxiuma and minimum condition, are the largest and smallest value of the function, are the condition when the value is either maxium or minimum. It can be in spesific range or in the entire domain of the function. I just watch the video material from youtube. https://www.youtube.com/watch?v=V239IIoGVT8

faridaan88 — 2019-04-08 05:04:45 UTC

Hope it can help your understanding

-Maximum and Minimum Condition of Function of Two (or more) Variable-

samsiatulkhusna280215 — 2019-04-08 06:00:29 UTC

The maximum and minimum of a function is very useful in geometry, physics, mechanics, and other fields. Maximum and minimum of function of two (or more) variable is simply talking about the partial derivatives of a function to find its maximum and minimum. Every function that has two or more variables has a local maximum at point (a,b) if f(x,y) ≤ f(a,b) for all points (x,y) in some disk with center (a,b). Then, the value of f(a,b) is called a local maximum value of f. According to Calculus III e-book, we can know the theorem for finding the maximums and minimums:
Theorem : If f is differentiable and has a local maximum or minimum at (a,b),
then fx(a,b) = 0 and fy(a,b) = 0.
For more explanation, you can kindly check this link: https://math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuides/vcalc/min_max/min_max.html
Thank you.

Maxim and minimum condition of function of two (or more) variables?

2019-04-08 07:39:42 UTC

A local maximum and minimum of the function is a point inside the domain when the value ia greater than the other point.

Maximum and Minimum Condition of function of two (or more) variables

hirzi_hadyanto — 2019-04-10 05:27:33 UTC

A local maximum and minimum of the function is a point inside the domain when the value is greater than the other point.

To decide the Local Maximum or Minimum of capacity we should to know experienced in geometry, mechanics, material science, and different fields, and was one of the persuading factors in the improvement of the math

In Local Maximum and Minimum Condition we will find out about The Second Derivatives.

The Second Derivative is utilized to decide whether a basic point is a relative Maximum or relative Minimum.