We have changed our privacy policy. In addition, we use cookies on our website for various purposes. By continuing on our website, you consent to our use of cookies. You can learn about our practices by reading our privacy policy.
© 2016 Shmoop University, Inc. All rights reserved.
Derivatives

Derivatives

Rolle's Theorem Examples

Example 1

Let f(x) = x2. Prove that there is some c in (-2, 2) with f ' (c) = 0.

Example 2

For the function f shown below, determine if we're allowed to use Rolle's Theorem to guarantee the existence of some c in (a, b) with f ' (c) = 0. If not, explain why not.

Example 3

Let . Determine if Rolle's Theorem guarantees the existence of some c in (-1, 1) with f ' (c) = 0. If not, explain why not.

Example 4

Let f(x) = x2x. Does Rolle's Theorem guarantees the existence of some c in (0, 1) with f ' (c) = 0? If not, explain why not.