1. Mean Value Theorem

2. Mean Value Theorem
Suppose f(x)=

3. Mean Value Theorem
Suppose f(x)= x y
0 0

4. Mean Value Theorem
Suppose f(x)= x y
0 0
1 1

5. Mean Value Theorem
Suppose f(x)= x y
0 0
1 1
2 8

6. Mean Value Theorem
Suppose f(x)= x y
0 0
1 1
2 8
-1 -1

7. Mean Value Theorem
Suppose f(x)= x y
0 0
1 1
2 8
-2 -8

8. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y 0 0
0 0
1 1
2 8
-2 -8

9. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y
Draw line from -2 to 2
0 0
1 1
2 8
-2 -8

10. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y
Draw line from -2 to 2
0 0
1 1
2 8
-2 -8

11. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y
Draw line from -2 to 2
0 0
Find slope of line:
1 1
2 8
-2 -8

12. Mean Value Theorem Suppose f(x)= (2,8) F(x) is continuous on [-2,2] xy
Draw line from -2 to 2
0 0
Find slope of line:
1 1
2 8
-2 -8
(-2,-8)

13. Mean Value Theorem Suppose f(x)= (2,8) F(x) is continuous on [-2,2] xy
Draw line from -2 to 2
0 0
Find slope of line:
1 1
2 8
-2 -8
(-2,-8)

14. Mean Value Theorem Suppose f(x)= (2,8) F(x) is continuous on [-2,2] xy
Draw line from -2 to 2
0 0
Find slope of line:
1 1
2 8
-2 -8
(-2,-8)

15. Mean Value Theorem Suppose f(x)= (2,8) F(x) is continuous on [-2,2] xy
Draw line from -2 to 2
0 0
Find slope of line:
1 1
2 8
Find derivative and set = 4
-2 -8
(-2,-8)

16. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y
Draw line from -2 to 2
Find slope of line:
0 0
1 1
2 8
-2 -8
Find derivative and set = 4

17. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y
Draw line from -2 to 2
Find slope of line:
0 0
1 1
2 8
-2 -8
Find derivative and set = 4

18. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y
Draw line from -2 to 2
Find slope of line:
0 0
1 1
2 8
-2 -8
Find derivative and set = 4

19. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y
Draw line from -2 to 2
Find slope of line:
0 0
1 1
2 8
-2 -8
Find derivative and set = 4

20. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y
Draw line from -2 to 2
Find slope of line:
0 0
1 1
2 8
-2 -8
Find derivative and set = 4

21. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y
Draw line from -2 to 2
Find slope of line:
0 0
1 1
2 8
-2 -8
Find derivative and set = 4
Draw tangent lines

22. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y
Draw line from -2 to 2
Find slope of line:
0 0
1 1
2 8
-2 -8
Find derivative and set = 4
Draw tangent lines

23. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y
Draw line from -2 to 2
Find slope of line:
0 0
1 1
2 8
-2 -8
Find derivative and set = 4
Draw tangent lines

24. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y
Draw line from -2 to 2
Find slope of line:
0 0
1 1
2 8
-2 -8
Find derivative and set = 4

25. Mean Value Theorem Suppose f(x)= F(x) is continuous on [-2,2] x y
Draw line from -2 to 2
Find slope of line:
0 0
1 1
2 8
-2 -8
Find derivative and set = 4