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6 Let a b be real numbers and f a b R a function We...

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6 Let a b be real numbers and f a b R a function We say that f is Lipschitz on a b if and only if the following statement is true EL 0 such that f x f y Lx y Vx y a b a Prove that if f a b R is Lipschitz on a b then f is uniformly continuous on a b b Suppose f a b R is differentiable Assume moreover that its derivative f is bounded on a b i e there is some M 0 such that f x M for every x a b Prove that f is Lipschitz on a b Hint Mean Value Theorem

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