Question: Let f(x) be a continuous function on the closed interval [a, b] and differentiable on the open interval (a, b). Prove that if f(a)

Let f(x) be a continuous function on the closed interval [a, b] and differentiable on the open interval (a, b). Prove that if f(a) = f(b) and f'(x) > 0 for all x in (a, b), then there exists a point c in (a, b) such that f(c) > f(x) for all x in (a, b), x * c

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