1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Mean Value Theorem Section 4.2

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 2 Quick Review

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 3 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.

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 4 Mean Value Theorem for Derivatives

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 5 Example Explore the Mean Value Theorem

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 6 Increasing Function, Decreasing Function

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 7 Corollary: Increasing and Decreasing Functions

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 8 Example Determining Where Graphs Rise or Fall

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 9 Corollary: Functions with f’=0 are Constant

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 10 Corollary: Functions with the Same Derivative Differ by a Constant

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 11 Antiderivative

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 12 Example Finding Velocity and Position

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Page 192 (1-19 odd) =================== Page 192 (21-33 odd, 39) Slide 4- 13