If f(x)=e^ x in [0, ], then c in Rolle's theorem is : - Vidyadip

MCQ

If $\text{f}(\text{x})=\text{e}^{\text{x}}\sin\text{x}$ in $[0,\pi],$ then $c$ in Rolle's theorem is :

A
$\frac{\pi}{6}$
B
$\frac{\pi}{4}$
C
$\frac{\pi}{2}$
✓
$\frac{3\pi}{4}$

✓

Answer

Correct option: D.

$\frac{3\pi}{4}$

$\text{f}(\text{x})=\text{e}^{\text{x}}\sin\text{x}$
$\text{f}\ '(\text{x})=\text{e}^{\text{x}}\cos\text{x}+\text{e}^{\text{x}}\sin\text{x}$
$\text{f}\ '(\text{c})=0$
$\text{e}^\text{c}(\cos\text{c}+\sin\text{c})=0$
$\cos\text{c}+\sin\text{c}=0$
$\cos\text{c}=-\sin\text{c}$
$\tan\text{c}=-1$
$\text{c}=\frac{3\pi}{4}\in(0,\pi)$

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