Question: Prove the given theorem and provide (1) examples. Theorem 1.5 (Mean - value theorem for derivatives) If f (x) is continuous in [a, b] and

b] and f'(x) exists in (a, b), then there exists at least

one value of x, say , between a and b such that

Prove the given theorem and provide (1) examples. Theorem 1.5 (Mean - value theorem for derivatives) If f (x) is continuous in [a, b] and f'(x) exists in (a, b), then there exists at least one value of x, say , between a and b such that f' (5) = 1(b) - f(a) a

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