Question.4. Suppose f:[0,1]->R is Differentiable function. If f(0)=0, f(x)=0 for all x belongs (0,1), then which of the following is necessarily true - ( Differentiability )

(A) f'(c)/f(c)=f'(1-2c)/f(1-2c) for at least one c belongs (0,1/2)

(B) f'(c)/f(c)=f'(1-3c)/f(1-3c) for at least one c belongs (0,1/3)

(C) f'(c)/f(c)=3f'(1-3c)/2f(1-3c)+1/(1-2c) for at least one c belongs (0,1/3)

(D) f'(c)/f(c)=3f'(1-3c)/2f(1-3c)+1/(1-2c) for at least one c belongs (1/3,1/2)