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