Discussion
Rolle's theorem requires, over and above continuity on the closed interval and differentiability on the open one,
Answer: A
Rolle's theorem asks for \( f(a) = f(b) \), and concludes that \( f'(c) = 0 \) for some \( c \) between them. Nothing is asked of the sign of the derivative, of monotonicity, or of where the interval sits: dropping the endpoint condition gives Lagrange's theorem instead, whose conclusion is a slope rather than a zero
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