Let f be a function that satisfies the following three hypotheses: 1. f is continuous on...

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Let f be a function that satisfies the following three hypotheses: 1. f is continuous on the closed interval [a, b]. 2. f is differentiable on the open interval (a, b). 3. f(a) = f(b) Then there is a number c in (a, b) such that f'(c) = 0. Let f be a function that satisfies the following three hypotheses: 1. f is continuous on the closed interval [a, b]. 2. f is differentiable on the open interval (a, b). 3. f(a) = f(b) Then there is a number c in (a, b) such that f'(c) = 0.

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SOLUTION The given hypotheses state that f is continuous on the c... View the full answer