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

Question

$(a)\;f^{'}(c)=g^{'}(c) \qquad(b)\;f^{'}(c)=2g^{'}(c)\qquad(c)\;2f^{'}(c)=g^{'}(c)\qquad(d)\;2f^{'}(c)=3g^{'}(c)$