If $f$ and $g$ are differentiable functions in $[0,1]$ satisfying $f(0)=2=g(1), g(0)=0$ and $f(1)=6$

Question

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 $c \in] 0,1[$\

Professor PC Thomas Classes · Answer

(c) : $\frac{f^{\prime}(c)}{g^{\prime}(c)}=\frac{f(1)-f(0)}{g(1)-g(0)}$ $=\frac{6-2}{2-0}=2 \Rightarrow f^{\prime}(c)=2 g^{\prime}(c)$\