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

If f is 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) + cf(c) = 0` c)`f'(c) - cf(c) = 0` d)`cf'(c) + f(c) = 0`

A

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

B

`f'(c) + cf(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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