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Question: Let f(x) and g(x) be differentiable in [0, 1] such that f(0) = 2, g(0) = 0, f(1) = 6. Let there exis...

Let f(x) and g(x) be differentiable in [0, 1] such that f(0) = 2, g(0) = 0, f(1) = 6. Let there exist a real number c in (0, 1) such that f ¢(3) = 2g¢(3), then g(1) =

A

1

B

– 1

C

2

D

– 2

Answer

2

Explanation

Solution

f ¢(3) = 2g¢(3), f(1)−f(0)1−0=2(g(1)−g(0))1−0\frac{f(1) - f(0)}{1 - 0} = \frac{2(g(1) - g(0))}{1 - 0}