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

Rolle's theorem is not applicable to $f(x)$ on $[0, \pi]$

Clearly, $f(x)$ is continuous on $[0, \pi]$ and differentiable on $(0, \pi)$ such that $f(0)=f(\pi)=0$.

So, Rolle's theorem is applicable to $f(x)$ on $[0, \pi]$.

Hence, option (d) is not correct.