Question: Prove the following Extended Mean Value Theorem. If and ' are continuous on the closed interval [a, b], and if exists in the

Prove the following Extended Mean Value Theorem. If ƒ and ƒ' are continuous on the closed interval [a, b], and if ƒ" exists in the open interval
(a, b), then there exists a number c in (a, b) such that

(b) = f(a) + f'(a)(b a) + (c)(b a). - -

(b) = f(a) + f'(a)(b a) + (c)(b a). - -

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