If and are differentiable functions on satisfying ,

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

Problem

If ff and gg are differentiable functions on (0,1)(0,1) satisfying f(0)=2=g(1)f(0)=2=g(1), g(0)=0g(0)=0, and f(1)=6f(1)=6, then for some c∈[0,1]c\in[0,1] (1) 2f′(c)=g′(c)2f'(c)=g'(c) (2) 2f′(c)=3g′(c)2f'(c)=3g'(c) (3) f′(c)=g′(c)f'(c)=g'(c) (4) f′(c)=2g′(c)f'(c)=2g'(c)

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