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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.

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