1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Connecting f ’ and f ” with the Graph of f Section 4.3

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 Quick Review asymptotes

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 4 What you’ll learn about First Derivative Test for Local Extrema Concavity Points of Inflection Second Derivative Test for Local Extrema Learning about Functions from Derivatives …and why Differential calculus is a powerful problem-solving tool precisely because of its usefulness for analyzing functions.

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 5 First Derivative Test for Local Extrema

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 6 First Derivative Test for Local Extrema

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 7 Example Using the First Derivative Test

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 8 Concavity

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 9 Concavity

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 10 Concavity Test

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

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 12 Point of Inflection

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 13 Example Finding Points of Inflection

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 14 Second Derivative Test for Local Extrema

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 15 Example Using the Second Derivative Test

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 16 Learning about Functions from Derivatives

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Pages 203-204 (1-29 odd) ==================== Pages 203-204 (2-30 even) ==================== Pages 204-205 (31-33, 37, 39, 41, 45) Slide 4- 17