Rolle's Theorem Examples
Example 1
Let f(x) = x^{2}. 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) = x^{2} – x. Does Rolle's Theorem guarantees the existence of some c in (0, 1) with f ' (c) = 0? If not, explain why not. |