If `f(x)` and `g(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` `f^(prime)(x)=0` for all `x` `f^(prime)(x)+4g^(prime)(x)=0` for at least one `x` `f(x)=2g'(x)` for at most one `x` none of these

Options

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

Answer

B