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If f is continuous on [a, b], differentiable on (a, b), and f(a) = f(b), Rolle's theorem gives
Af'(c) = f(a) at some c
Bf constant on [a, b]
Cf'(c) = 0 for some c
Df(c) = 0 at some c
Answer & Solution
Correct answer: C. f'(c) = 0 for some c
Equal end values force the graph to turn somewhere inside, where the tangent is horizontal.
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