1. Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH
From left to right

2. 1 2 Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH
f ’(x) > 0 for all x in I 2
f(x) increasing
Increasing\Decreasing
f ’ (x) < 0 for all x in I
f(x) decreasing

3. Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH

4. Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH

5. Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH
How to find local max and local min

6. _ _ + + 1 2 1 2 Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH
First Derivative Test: 1 _ + 2
First Derivative Test: 1 _ + 2

7. Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH_ + + + + + + + _ _ + + _ + + +

8. Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH

9. Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH

10. Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH

11. _ _ + + 1 2 1 2 Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH
First Derivative Test: 1 _ + 2
First Derivative Test: 1 _ + 2

12. Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH_ + + + + + + + _ _ + + _ + + +

13. Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH
Example:
Find all local max and local min

14. Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH

15. Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH
Example:
Find all local max and local min