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 $c \in] 0,1[:$
$2 f^{\prime}(c)=g^{\prime}(c)$
$2 f^{\prime}(c)=3 g^{\prime}(c)$
$f^{\prime}(c)=g^{\prime}(c)$
$f^{\prime}(c)=2 g^{\prime}(c)$
Correct Option: , 4
Solution:
