Q. The function $f(x) = a\sin{x + \frac{1}{3}\sin{3x}}$ has maximum value at$x = \frac{\pi}{3}$. The value of $a$ is
A) 3
B) 1/3
C) 2
D) 1/2
Explanation
(c)
Since, $f(x) = a\sin x + \frac{1}{3}\sin{3x}$ has maximum at $x = \frac{\pi}{3}$
$\therefore\ \ \ f'\left( \frac{\pi}{3} \right) = 0\$ $\Rightarrow \ \ \ \ \ \ a\cos\frac{\pi}{3} + \cos\pi = 0$
$\Rightarrow \ \ \ \ \ a = 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.