Let be differentiable on with ,

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Let ff be differentiable on [0,6][0,6] with f(0)=2f(0)=2, f(3)=8f(3)=8, and f(6)=2f(6)=2. Which of the following must be true? (a) There exists ee in (3,6)(3,6) such that f′(e)=2f'(e)=2. (b) There exists cc in (0,3)(0,3) such that f′(c)=1f'(c)=1. (c) There exists dd in (0,6)(0,6) such that f′(d)=0f'(d)=0. (d) f′(x)<0f'(x)<0 for all xx in (3,6)(3,6).

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