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Derivatives

Derivatives

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 f(x) = \frac{1}{x2}. 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) = x2 - x. Determine if 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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