1. AP Calculus Honors Ms. Olifer
Connecting f ’ and f ” with the graph of f
AP Calculus Honors Ms. Olifer

2. 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.

3. First Derivative Test for Local Extrema

4. First Derivative Test for Local Extrema

5. Example Using the First Derivative Test

6. Concavity

7. Concavity

8. Concavity Test

9. Example Determining Concavity

10. Point of Inflection

11. Example Finding Points of Inflection

12. Second Derivative Test for Local Extrema

13. Example Using the Second Derivative Test

14. Learning about Functions from Derivatives