1. Connecting f′ and f″ with the graph of f
Chapter 5
Applications of Derivatives
Section 5.3
Connecting f′ and f″
with the graph of f

2. Quick Review

3. Quick Review

4. Quick Review Solutions

5. Quick Review Solutions

6. What you’ll learn about
Intervals of increase or decrease
Both First and Second Derivative Tests for local extrema
Intervals of upward or downward concavity
Points of inflection
Identification of key features of functions and their derivatives
…and why
Differential calculus is a powerful problem-solving
Tool precisely because of its usefulness for
analyzing functions.

7. First Derivative Test for Local Extrema

8. First Derivative Test for Local Extrema

9. First Derivative Test for Local Extrema

10. First Derivative Test for Local Extrema

11. First Derivative Test for Local Extrema

12. First Derivative Test for Local Extrema

13. First Derivative Test for Local Extrema

14. Example Using the First Derivative Test

15. Concavity

16. Concavity

17. Concavity Test

18. Example Determining Concavity

19. Point of Inflection

20. Example Finding Points of Inflection

21. Second Derivative Test for Local Extrema

22. Example Using the Second Derivative Test

23. Learning about Functions from Derivatives

24. Quick Quiz for Sections 5.1 – 5.3

25. Quick Quiz for Sections 5.1 – 5.3

26. Quick Quiz for Sections 5.1 – 5.3

27. Quick Quiz for Sections 5.1 – 5.3

28. Quick Quiz for Sections 5.1 – 5.3

29. Quick Quiz for Sections 5.1 – 5.3