Mathematics

Mathematics

Problem

If ff is a continuous function on [0,1][0, 1], differentiable in (0,1)(0, 1) such that f(1)=0f(1) = 0, then there exists some c∈(0,1)c \in (0, 1) such that (a) cf′(c)−f(c)=0cf'(c) - f(c) = 0 (b) f′(c)+cf(c)=0f'(c) + cf(c) = 0 (c) f′(c)−cf(c)=0f'(c) - cf(c) = 0 (d) cf′(c)+f(c)=0cf'(c) + f(c) = 0 (a) cf′(c)−f(c)=0cf'(c) - f(c) = 0 (b) f′(c)+cf(c)=0f'(c) + cf(c) = 0 (c) f′(c)−cf(c)=0f'(c) - cf(c) = 0 (d) cf′(c)+f(c)=0cf'(c) + f(c) = 0

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