1. Applications of Derivatives
Chapter 4
Applications of Derivatives

2. What you’ll learn about
4.1
Extreme Values of Functions
Homework: pg.193 #1(ex.1), 3(ex. 2), 11 (ex.3)
review: solve inequality: pg.18 quick review # 1, 2, 6
What you’ll learn about
Absolute (Global) Extreme Values
Local (Relative) Extreme Values
Finding Extreme Values
…and why
Finding maximum and minimum values of a
function, called optimization, is an important
issue in real-world problems.

3. What you’ll learn about
Absolute (Global) Extreme Values
Local (Relative) Extreme Values
Finding Extreme Values
…and why
Finding maximum and minimum values of a
function, called optimization, is an important
issue in real-world problems.

4. Match the table with the graph:

8. Example1

9. Example2

14. Example Finding Absolute Extrema
Find critical points
Find critical points values
Endpoints values
Chose max and min values which are absolute extremas

15. Example Finding Extreme Values

16. Homework: # 22, 25 pg.194 pg.18 quick review # 3, 4, 5
2/19/2013 Extreme Values of Functions
Objectives: Absolute (Global) Extreme Values Local (Relative) Extreme Values Finding Extreme Values
Homework: # 22, 25 pg.194
pg.18 quick review # 3, 4, 5
While a function’s extrema can occur only at critical points and endpoints, not every critical point or endpoint signals the presence of an extreme value.

17. Read example 4 pg. 190, solve # 27, 28 pg.194
Example 6 read together, exploration 1 (optional)

18. Mean Value Theorem Homework: pg.202 #1(ex.1), 4
4.2
Mean Value Theorem
Homework: pg.202 #1(ex.1), 4

19. What you’ll learn about
Mean Value Theorem
Physical Interpretation
Increasing and Decreasing Functions
Other Consequences
…and why
The Mean Value Theorem is an important theoretical
tool to connect the average and instantaneous rates of
change.

21. Continuous? Differentiable?

22. Example Explore the Mean Value Theorem

23. # pg. 202

24. Objectives: Mean Value Theorem Physical Interpretation
Increasing and Decreasing Functions
Homework: pg.202 # 15, 20, 26
Objectives: Mean Value Theorem
Physical Interpretation
Increasing and Decreasing Functions
Other Consequences
…and why
The Mean Value Theorem is an important theoretical
tool to connect the average and instantaneous rates of
change.

25. Increasing Function, Decreasing Function

26. Corollary: Increasing and Decreasing Functions

27. Example Determining Where Graphs Rise or Fall

28. First Derivative Test for Local Extrema

29. First Derivative Test for Local Extrema

30. Example Using the First Derivative Test
solve # 16, 22, 18, 21, 25 pg.202

31. 4.2 Other Consequences
Objectives: Mean Value Theorem Physical Interpretation Increasing and Decreasing Functions
Other Consequences
Homework: read example 7 pg.200 solve # 35, 38, 43 (pg. 203)

32. Corollary: Functions with f’=0 are Constant

33. Corollary: Functions with the Same Derivative Differ by a Constant

34. Antiderivative

35. Example Finding Velocity and Position

36. Example 5 pg.,