Find the maximum and minimum of
Question:

Find the maximum and minimum of

$f(x)=\left(\sin x+\frac{1}{2} \cos x\right)$ in $0 \leq x \leq \frac{\pi}{2}$

Solution:

max. value is $\frac{3}{4}$ at $x=\frac{\pi}{6}$ and min. value is $\frac{1}{2}$ at $x=\frac{\pi}{2}$