(See Solution) Suppose that f is continuous on [ a, b ] and differentiable on (a , b), and that f'(x) is never zero at any point on (a , b). Explain


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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