Question

The function $f\left(x\right)=a\sin x+\frac{1}{3}\sin 3x$ has a maximum at $x=\pi /3$, then a equals-

• A. $-2$
• B. $2$
• C. $-1$
• D. $1$

Answer 1

The correct option is B $2$

$\begin{array}{c}f\left(x\right)=a\sin x+\frac{1}{3}\sin 3x\\ f^{{}^{\prime }}\left(x\right)=a\cos x+\frac{1}{3}\cos 3x\times 3\\ =a\cos x+\cos 3x\\ Sincef\left(x\right)hasmaximumatx=\frac{\pi }{3}\\ so,f^{\prime }\left(\frac{\pi }{3}\right)=0\\ \Rightarrow a\cos \frac{\pi }{3}+\cos 3\times \frac{\pi }{3}=0\\ \Rightarrow a\times \frac{1}{2}+\left(-1\right)=0\\ \Rightarrow \frac{a}{2}=1\\ a=2\end{array}$