Question

The function $f\left(x\right)=\frac{x}{2}+\frac{2}{x},x>0$ has a local minimum at

• A. $x=2$
• B. $x=-2$
• C. $x=0$
• D. $x=1$

Answer 1

The correct option is A $x=2$

Given, $f\left(x\right)=\frac{x}{2}+\frac{2}{x}$

$\frac{x}{2}+\frac{2}{x}$ is of the form $x+\frac{1}{x}\ge 2$ and equality holds for $\frac{x}{2}=\frac{2}{x}$

Hence, option A is correct.