The value of $c \in [0, \pi ]$ for which the function $f(x)=e^x\, sin x $ satisfies Rolle's theorem is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $\frac{3\pi}{4}$
$f(0)=0$ $f(π)=0$
so for some c $f'(c)=0$
$f'(x)=e^x(\sin x+\cos x)=0$ (at $x=c$)
so $\sin c+\cos c=0$
$⇒c=\frac{3\pi}{4}$