1. Optimization
Rizzi – Calc BC

2. Quiz Recap
When looking for absolute extrema on a closed interval, CHECK ENDPOINTS
Check answers to make sure they’re in the given interval
Check your basic algebra
Graphs of f’ will continue to be important

3. Optimization
Refers to finding maximum or minimum values of SOMETHING based on certain constraints.
Key Words:
Greatest profit
Least cost
Greatest voltage
Optimum size
Shortest distance

4. Simple Problem
Using a piece of 8.5x11” paper, I want to cut out squares from each corner to create a box with maximum volume. How big should the squares be?

5. Guidelines for Optimization
Identify all given quantities and all quantities to be determined. Draw a picture.
Write a primary equation for the quantity that is to be optimized.
Reduce the primary equation to be in terms of a single variable, using secondary equations if necessary.
Determine the feasible domain for the primary equation. What makes sense?
Determine the desired max or min value by using first and second derivative tests.

6. Try it!
A manufacturer wants to design an open box having a square base and a surface area of 108 square inches. What dimensions will produce a box with maximum volume?

7. One more
Which points on the graph of the function are closest to the point (0, 2)?

8. AP Question C