Question

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

• A. $1$
• B. $-1$
• C. $0$
• D. $2$

Answer 1

The correct option is D $2$

$f^{\prime }\left(x\right)=acosx+cos3x$
$f^{\prime }\frac{\pi }{3}=0$ (at extremum $f^{\prime }\left(x\right)=0)$
$a\left(\frac{1}{2}\right)-1=0$
$a=2$