Paul's Online Math Notes
Calculus I (Assignment Problems) / Applications of Derivatives / The Mean Value Theorem   [Notes] [Practice Problems] [Assignment Problems]

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

Calculus I (Assignment Problems) / Applications of Derivatives / The Mean Value Theorem    [Notes] [Practice Problems] [Assignment Problems]

© 2003 - 2017 Paul Dawkins