Question

f(x) = sin x (1 + cosx) has maximum value at x=

• A. 0
• B. $\pi$
• C. $\frac{\pi }{3}$
• D. 1

Answer 1

Answer: (C)

$\frac{\pi }{3}$

$f\left(x\right)=\sin x\left(1+\cos x\right)f\left(x\right)=\sin x+\frac{1}{2}\sin 2x$

On differentiating w.r.t $x$, we get

$f^{{}^{\prime }}\left(x\right)=\cos x+\cos 2x$

Therefore,

$\cos x+2{\cos }^{2}x-1=02{\cos }^{2}x+\cos x-1=02{\cos }^{2}x+2\cos x-\cos x-1=0\left(2\cos x-1\right)\left(\cos x+1\right)=0\cos x=-1or\cos x=\frac{1}{2}$

$Clearlymaximumoccursatx=\frac{\pi }{3}$

$Hence,optionCiscorrectanswer.$