4­4 Modeling and Optimization
*Derivative Application
Strategies for solving Max/Min Problems
1. Understand the problem. Are you looking for a maximum or a minimum?
2. What is being maximized or minimized?
3. Write an expression (usually in one variable) for what is being maximized or minimized.
4. Find critical values for the expression.
5. Justify the max or min. Usually NLA.
6. Answer the question!!!!
7. And the best part of max/min problems: if possible, draw a picture.
1
Example:
What is the smallest possible perimeter for a rectangle whose area is 16 m2?
2
Example:
A rectangular plot is to be bounded on one side by a river. If you have 800 feet of fence, find the dimensions of the plot that give the maximum area.
3
Example:
The sum of two nonnegative numbers is 20. Find the numbers if the sum of their squares is to be a) as large as possible
b) as small as possible
4
Page 226 #1, 5, 9, 12, 17
5
6
7
#20
x
6 ‑ x
8
Page 228 #27, 41
Read over questions 57 ­ 65
9
10
11