Question

Find maximum value of $f\left(x\right)=\sin x+\sqrt{3}\cos x$

Answer 1

Consider the following question.

$f\left(x\right)=sinx+\sqrt{3}\cos x$

Differentiate$f\left(x\right)$ with respect to$x$ we get,

$f^{{}^{\prime }}\left(x\right)=\cos x-\sqrt{3}\sin x$

$f^{{}^{\prime }}\left(x\right)=0$

$\cos x-\sqrt{3}\sin x=0$

$\tan x=\frac{1}{\sqrt{3}}$

$x=\frac{\pi }{6}$

$f^{\prime \prime }\left(x\right)=-sinx-\sqrt{3}\cos x$

$f^{\prime \prime }\left(x\right)=-sin\frac{\pi }{6}-\sqrt{3}\cos \frac{\pi }{6}$

$=-\frac{1}{2}-\frac{3}{2}$

$=-2$

Hence, it is a maxima.

Hence, this is the correct answer .