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

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

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

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?

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.

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.

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

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