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If `f(x)a n dg(x)` are differentiable functions for `0lt=xlt=1` such that `f(0)=10 ,g(0)=2,f(1)=2,g(1)=4,` then in the interval `(0,1)dot` (a) `f^(prime)(x)=0 for a l lx` (b) `f^(prime)(x)+4g^(prime)(x)=0` for at least one `x` (c) `f(x)=2g'(x)` for at most one `x` (d) none of these

A

`f(x)=0` for all x

B

`f(x)+4g'(x)=0` for at least one x

C

`f(x)=2g'(x)` for at most one x

D

none of these

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The correct Answer is:
B
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