Mathematics HL- Maxima and Minima by Nathan

Knowledge and Skills Inventory

nthnkim — 2015-12-09 05:51:18 UTC

Academic Honesty

nthnkim — 2015-12-09 05:57:33 UTC

Make sure to acknowledge sources of information correctly and properly.

http://www.citefast.com/

2015-11-25 00:14:35 UTC

2015-11-25 00:14:09 UTC

nthnkim — 2015-11-24 23:53:35 UTC

2015-11-16 10:32:41 UTC

2015-11-11 03:01:11 UTC

2015-11-11 03:01:09 UTC

nthnkim — 2015-11-10 23:37:55 UTC

IB Learner Profile

nthnkim — 2015-11-10 03:51:36 UTC

Inquirers, Knowledgeable, Thinkers, Communicators, Principled, Open-minded, Caring, Risk-takers, Balanced, and Reflective

http://www.ibo.org/globalassets/digital-tookit/flyers-and-artworks/learner-profile-en.pdf

ATL SKills

nthnkim — 2015-11-10 01:48:45 UTC

a. Thinking Skills

b. Communications Skills

c. Social Skills

d. Self-management Skills

e. Research Skills

Blackboard

nthnkim — 2015-11-10 01:27:18 UTC

First, we should be on the same network, TOMLALALA

Copy and paste the address given below to the address of your chosen web browser. BTW it supports only HTML 5 based browsers.

http://192.168.11.4:8080

Read it first

nthnkim — 2015-11-10 01:19:58 UTC

This wall will be archived every day for formative assessment purpose. Your contributions are always welcome.

Real-world Problem: The eight failures that caused the Gulf oil spill

nthnkim — 2016-03-20 05:51:00 UTC

Eight catastrophic failures led to the explosion that destroyed the Deepwater Horizon drilling rig in the Gulf of Mexico, killing 11 people and leading to one of the biggest oil leaks in history, according to BP’s long-awaited investigation into the accident.

BP accepts its role in the disaster but also points the finger at two of its contractors.

The accident occurred on 20 April as the team aboard Deepwater Horizon was preparing to temporarily abandon a well it had drilled some 70 kilometres from the US coast.

The day before the accident, the crew had pumped cement to the bottom of the borehole, a standard procedure intended to prevent oil leaking out. On the day of the accident, the team were conducting checks to determine that that the well had been properly sealed.

Pressure test misinterpreted

The crew carried out various pressure tests to determine whether the well was sealed or not. The results of these tests were misinterpreted, so they thought the well was under control.
https://www.newscientist.com/article/dn19425-the-eight-failures-that-caused-the-gulf-oil-spill/

Model Develop

nthnkim — 2016-03-20 05:51:16 UTC

f(x)=e^(x^2) cos(50x)
Graph it using GDC
What is the maximum/minimum?

Model Test

nthnkim — 2016-03-20 05:51:32 UTC

Find stationary points

Apply

nthnkim — 2016-03-20 05:51:53 UTC

Locate the position and nature of any turning points of the following function:

Reflect

nthnkim — 2016-03-20 05:52:13 UTC

Where is the peak? And How do we know it?

nthnkim — 2016-03-20 06:09:47 UTC

Image from http://static.panoramio.com/photos/large/20268917.jpg

First order derivative

nthnkim — 2016-03-20 07:00:08 UTC

The derivative provides information about the gradient of a function. And we can use it to locate points on a graph where the gradient is ZERO: stationary point
Concave Up: Local Maximum
Concave Down: Local Minimum

Second order derivative

nthnkim — 2016-03-20 07:01:23 UTC

Derivative of dy/dx is called the second derivative
Distinguishing maximum points from minimum points

Conjecture 1.

nthnkim — 2016-03-21 11:58:05 UTC

If dy/dx=0, then max or min.

Conjecture 2.

nthnkim — 2016-03-21 12:16:31 UTC

If dy/dx, gradient of tangent line, is decreasing near the stationary point then the point must be minimum. In other words, if the derivative of dy/dx is decreasing. This means the stationary point is a maximum.
If the second derivative is negative(positive) at a stationary point, the point must be maximum(minimum).

Behaviour of

nthnkim — 2016-03-21 13:38:16 UTC

Change in dy/dx

nthnkim — 2016-03-21 13:45:15 UTC

First order derivati

nthnkim — 2016-03-21 14:00:34 UTC

Second order derivative

nthnkim — 2016-03-21 14:06:56 UTC

Another example

nthnkim — 2016-03-21 14:14:08 UTC

First order derivative

nthnkim — 2016-03-21 14:16:43 UTC

Finding Stationary Points

Second order derivative

nthnkim — 2016-03-21 14:19:03 UTC

Maximum and minimum

Extend

nthnkim — 2016-03-21 14:22:19 UTC

nthnkim — 2016-03-21 14:25:01 UTC

nthnkim — 2016-03-21 14:25:55 UTC

nthnkim — 2016-03-21 14:28:35 UTC

nthnkim — 2016-03-22 06:46:00 UTC

nthnkim — 2016-03-22 07:02:47 UTC