A function f is defined by $f\left(x\right)=e^x\sin x$ in $[0,\pi ]\text{. }$ Which of the following is not correct?

Clearly , $f\left(x\right)$ is continuous on  $[0,\pi ]$ and 

differentiable on $(0,\pi )$ such that $f\left(0\right)=f\left(\pi \right)=0$

So, Rolles theorem is applicable to   $f\left(x\right)$ on  $[0,\pi ]$

Hence, option (d) is not correct.