1. Chapter 5
Applications of Derivatives
Section 5.2
Mean Value Theorem

2. Quick Review

3. Quick Review Solutions

4. What you’ll learn about
The Mean Value Theorem
Increasing and decreasing functions
Functions whose derivative is zero
Antidifferentiation
…and why
The Mean Value Theorem is an important theoretical
tool to connect the average and instantaneous rates
of change.

5. Mean Value Theorem for Derivatives

6. Example Explore the Mean Value Theorem

7. Increasing Function, Decreasing Function

8. Corollary: Increasing and Decreasing Functions

9. Example Determining Where Graphs Rise or Fall

10. Corollary: Functions with f ′ = 0 are Constant

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

12. Antiderivative

13. Example Finding Velocity and Position