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

• A

  $2f^{\text{'}}\left(c\right)=g\left(c\right)$
• B

  $2f^{\text{'}}\left(c\right)=3g^{\text{'}}\left(c\right)$
• C

  $f^{\text{'}}\left(c\right)=g^{\text{'}}\left(c\right)$
• Correct answer
  D

  $f^{\text{'}}\left(c\right)=2g^{\text{'}}\left(c\right)$

Hence, the correct answer is option: 'D'.