1. Concavity f is concave up if f’ is increasing on an open interval. f is concave down if f’ is decreasing on an open interval.

2. Concavity Logically: If f’’ > 0 then f’ is increasing. If f’ is increasing, then f is concave up on the open interval. Therefore, if f’’ > 0 then f is concave up on the open interval.

3. Concavity

5. Point of Inflection

6. Basically, just like critical points are found when f’ is 0 or DNE, points of inflection are found when f’’ is 0 or DNE. Also, just like f is increasing or decreasing when f’ is >0 or 0 or <0.

7. Point of Inflection

8. Second Derivative Test