Q. The maximum value of $f(x) = \sin{x(1 + \cos x)}$ is
A) $\frac{3\sqrt{3}}{4}$
B) $\frac{3\sqrt{3}}{2}$
C) $3\sqrt{3}$
D) $\sqrt{3}$
Explanation
(a)
Given, $f(x) = \sin{x(1 + \cos x)}$
It is minimum at $x = \frac{\pi}{3}$
$\therefore f\left( \frac{\pi}{3} \right) = \sin\left( \frac{\pi}{3} \right)\left( 1 + \cos\frac{\pi}{3} \right)$
$= \frac{\sqrt{3}}{2}\left( 1 + \frac{1}{2} \right) = \frac{3\sqrt{3}}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.