1. 1 2 Sec4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH Concavity Test
f’’(x) > 0 for all x in I 2
f(x) concave Up
Concavity Test
f’’(x) < 0 for all x in I
f(x) concave Down

2. 1 2 Example: Discuss the curve with respect to concavity,
Sec4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH 1
f’’(x) > 0 for all x in I 2
f(x) concave Up
Concavity Test
f’’(x) < 0 for all x in I
f(x) concave Down
Example:
Discuss the curve
with respect to concavity,

3. Concavity Test 1
f’’(x) > 0 for all x in I
f(x) concave Up

4. Concavity Test 1
f’’(x) < 0 for all x in I
f(x) concave Down

5. Find all inflection points of
Sec4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH
Example:
Find all inflection points of

6. Sec4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH

7. F091

8. Example: x^(2n) true or false

9. F081

10. F083

11. F083

12. F091