1. AP Calculus March 10 and 13, 2017 Mrs. Agnew
Optimization
AP Calculus
March 10 and 13, 2017
Mrs. Agnew

2. Essential Question Essential Vocabulary
How do you find the absolute maximum and minimum of a function and how does that apply to real world situations?
Essential Vocabulary
Absolute Extrema
Optimization
Critical Numbers

3. Extreme Values What does the Extreme Value Theorem state?
What does Fermat’s Theorem state?
Inverse of Fermat’s Theorem?
Is it true?
Examples

4. Critical Numbers What are critical numbers and how do we find them?
Critical numbers are where derivative is zero or undefined
Horizontal and Vertical Tangent Lines
What is the relationship between critical numbers and extreme values?

5. Absolute Extrema
Given a closed interval of a graph, where could the absolute max/min occur?
To find ABSOLUTE max or min, compare critical points and endpoints of interval.

6. Optimization Problems
One of the most common applications of derivatives.
Allows us to find greatest profit, least cost, least time, greatest distance, least distance, optimum size, etc.
We are looking for absolute max/min to solve problem.

7. Optimization Problems
Steps in solving Optimization Problems:
Identify unknowns and given conditions
Draw diagram if necessary
Assign variables to given quantities and to quantity that will be maximized/minimized
Express quantities in equation
Compare critical points and endpoints to obtain optimization

8. Practice & Homework Guided Practice: page 312 – 317
#10, 12, 14, 16, 21
#More Examples & More
Suggested Homework
WS #11, 15, 16, 20, 21, 22, 25, 41
page 312 #6, 9