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Paul
August 7, 2018

Calculus I - Assignment Problems
 Derivatives Previous Chapter Next Chapter Integrals The Shape of a Graph, Part II Previous Section Next Section Optimization

## The Mean Value Theorem

For problems 1  4 determine all the number(s) c which satisfy the conclusion of Rolle’s Theorem for the given function and interval.

1.  on

2.  on

3.  on

4.  on

For problems 5  8 determine all the number(s) c which satisfy the conclusion of the Mean Value Theorem for the given function and interval.

5.  on

6.  on

7.  on [-1, 0].

8.  on

9. Suppose we know that  is continuous and differentiable on the interval ,  that  and that .  What is the smallest possible value for ?

10. Suppose we know that  is continuous and differentiable on the interval ,  that  and that .  What is the smallest possible value for ?

11. Suppose we know that  is continuous and differentiable on the interval ,  that  and that .  What is the largest possible value for ?

12. Suppose we know that  is continuous and differentiable on the interval ,  that  and that .  What is the largest possible value for ?

13. Show that  has exactly one real root.

14.  Show that  has exactly one real root.

15. Show that  has exactly one real root.

 The Shape of a Graph, Part II Previous Section Next Section Optimization Derivatives Previous Chapter Next Chapter Integrals

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