Practicing Success
Practicing Success
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The value of $c \in [0, \pi ]$ for which the function $f(x)=e^x\, sin x $ satisfies Rolle's theorem is : |
$\frac{\pi}{2}$ $\frac{\pi}{4}$ $\frac{\pi}{6}$ $\frac{3\pi}{4}$ |
$\frac{3\pi}{4}$ |
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 $\sin c+\cos c=0$ $⇒c=\frac{3\pi}{4}$ |
