Optimization Problems.

0:00 Optimization Problems.

First Derivative Test.

 Second Derivative Test.

Largest Possible Product.

Write the Objective Function as a Function of One Variable.

Maximum Area Rectangles.

Minimum Sum.

A Rectangular pen is built with one side against a barn.

 A rancher plans to make four identical and adjacent rectangular pens against a barn.

Rectangles beneath a Semicircle.

2:37 Example: What two non-negative real numbers with a sum of 30 have the largest possible product.

9:10 Example: Maximum Area Rectangles.

13:02 Example: Minimum Sum.

16:35 Example: A Rectangular Pen is built with one side against a Barn. What dimensions maximize the area of the Pen?

20:21 A Rancher plans to make four identical and adjacent Pens against a Barn.

25:47 Example: Rectangles beneath a Semicircle.

Optimization.

Find two positive numbers whose Product is 100 and whose Sum is a Minimum.

Optimization.

What is the Maximum Vertical Distance between y=x+2 and y=x^2 for x in [-1, 2].