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If f and g are differentiable functions in [0, 1] satisfying `f(0)""=""2""=g(1),g(0)""=""0` and `f(1)""=""6` , then for some `c in [0,""1]`
(1) `2f^'(c)""=g^'(c)`
(2) `2f^'(c)""=""3g^'(c)`
(3) `f^'(c)""=g^'(c)`
(4) `f'(c)""=""2g'(c)`

A

`2 f'(c) = g'(c)`

B

`2f'(c) = 3g'(c)`

C

`f'(c) = g'(c)`

D

`f'(c) = 2g'(c)`

Text Solution

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The correct Answer is:
D
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