If $f$ and $g$ are differentiable function in $[0, 1]$ satisfying $f(0)=2 = g(1),g(0)= 0$ and $f(1)=6$, then for some $c\in [0,1]$

Question

$\begin{array}{1 1}(A)\;2f'(c)=g'(c)\\(B)\;2f'(c)=3g'(c)\\(C)\;f'(c)=g'(c)\\(D)\;f'(c)=2g'(c)\end{array}$