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

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

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

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 5 Quick Review Solutions

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

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 7 First Derivative Test for Local Extrema

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 8 First Derivative Test for Local Extrema

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 9 Example Using the First Derivative Test

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

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

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 12 Concavity Test

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 13 Example Determining Concavity

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 14 Point of Inflection

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 15 Example Finding Points of Inflection

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 16 Second Derivative Test for Local Extrema

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 17 Example Using the Second Derivative Test

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 18 Learning about Functions from Derivatives

19. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 19 Quick Quiz for Sections 4.1-4.3

20. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 20 Quick Quiz for Sections 4.1-4.3

21. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 21 Quick Quiz for Sections 4.1-4.3

22. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 22 Quick Quiz for Sections 4.1-4.3

23. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 23 Quick Quiz for Sections 4.1-4.3

24. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 24 Quick Quiz for Sections 4.1-4.3