Review Session for AP Calculus

1. Applications of Derivatives
Optimization and Related Rates

2. Optimization
Finding Maximum and Minimum Values
First Derivative Test
Second Derivative Test

3. Extreme Value Theorem
If f is continuous on a closed interval [a, b] then f has both a minimum and a
maximum on the interval

4. Optimization
Multiple Choice Examples

5. Example 1

6. Answer 1

7. Example 2

8. Answer 2

9. Example 3

10. Answer 3

11. Example 4

12. Answer 4

13. Example 5

14. Answer 5

15. Hints for Related Rates Problems
–Draw appropriate picture if applicable
–Identify an appropriate formula
–Identify and know and unknown variables including rates of change,
express each rate of change as a derivative, identify what the question is
asking you to solve
–Plug in any unchanging variables to your formula, if you are unsure
wait to plug it in
–Differentiate your formula with respect to time
–Plug in for all remaining variables and solve for your unknown

16. Related Rates
Multiple Choice Examples

17. Example 6

18. Answer 6

19. Example 7

20. Answer 7

21. Example 8

22. Answer 8

23. Example 9

24. Applications of Derivatives
Free Response

29. Thanks for Attending
I hope that this presentation has been helpful.
Don’t forget about the upcoming sessions:
BC only, this Thursday 4/6 at 7 PM on Series
AB/BC combined next Monday 4/10 at 7 PM on Integration Techniques