Answer true or false. The Mean-Value Theorem guarantees there is at least one c on [0, 1] such that f '(x) = 0.8 when f(x) = x.

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The Mean Value Theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one c in (a, b) such that f'(c) = (f(b) - f(a)) / (b - a). For f(x) = x on [0, 1], f'(x) = 1 for all x in (0, 1), so there is no c in (0, 1) where f'(c) = 0.8.

Answer True or False