Review the MVT stated in Section 4.3 (Theorem 1, p. 231) and show how it can be used, together with the Fundamental Theorem of Calculus, to prove the MVT for Integrals.

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THEOREM 1 The Mean Value Theorem Assume that f is continuous on the closed interval [a, b] and differentiable on (a, b). Then there exists at least one value c in (a, b) such that f'(c) = f(b)-f(a) b-a