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If f be a continuous function on [0,1], ...

If f be a continuous function on [0,1], differentiable in (0,1) such that f(1) = 0 , then there exists some `c in (0,1)` such that

A

`cf'(c ) - f (c ) = 0 `

B

`f'(c ) + c f(c ) = 0 `

C

`f'(c ) -cf(c ) =0`

D

`cf'(c ) + f(c ) =0`

Text Solution

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The correct Answer is:
D
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