Question

The value of $a$ for which the function $f\left(x\right)=a\sin x+\frac{1}{3}\sin 3x$ has an extremum at $x=\frac{\pi }{3}$ is

• A. 2.00
• B. 2
• C. 2.0

Answer 1

Answer: (A), (B), (C)

$f\left(x\right)=a\sin x+\frac{1}{3}\sin 3x$
$\Rightarrow f^{\prime }\left(x\right)=a\cos x+\cos 3x$
For being an extremum at $x=\frac{\pi }{3}$
$f^{\prime }\left(\frac{\pi }{3}\right)=0$
$\Rightarrow a\cos \frac{\pi }{3}+\cos \pi =0$
$\Rightarrow \frac{a}{2}-1=0\Rightarrow a=2$