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

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 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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