Question

At $x=\frac{\pi }{3},f\left(x\right)=\sin x(1+\cos x)$ has

• A. maximum
• B. minimum
• C. neither maximum nor minimum
• D. None

Answer 1

The correct option is A maximum

Consider the given function.

$f\left(x\right)=\sin x(1+\cos x)$

Since,

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

Therefore,

$f\left(\frac{\pi }{3}\right)=\sin \frac{\pi }{3}(1+\cos \frac{\pi }{3})$

$f\left(\frac{\pi }{3}\right)=\frac{\sqrt{3}}{2}(1+\frac{1}{2})$

$f\left(\frac{\pi }{3}\right)=\frac{\sqrt{3}}{2}\left(\frac{3}{2}\right)$

$f\left(\frac{\pi }{3}\right)=\frac{3\sqrt{3}}{4}$

So, this is the maximum value of the given function.

Hence, this is the answer.