Suppose that f is continuous on [a, b] and differentiable on (a, b), and that f'(x) is never zero at
Question: Suppose that f is continuous on [a, b] and differentiable on (a, b), and that \(f'\left( x \right)\) is never zero at any point on (a, b). Explain why the maximum and minimum values must occur at the endpoints of the interval [a, b].
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