Question

The function $f\left(x\right)=\frac{x}{2}+\frac{2}{x}$ 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 $f\left(x\right)=\frac{x}{2}+\frac{2}{x}$, $f^{\prime }\left(x\right)=\frac{1}{2}-\frac{2}{x^2}$

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

$\Rightarrow$ $\frac{1}{2}-\frac{2}{x^2}=0$

$\Rightarrow$ $x\pm 2$

$f^{\prime \prime }\left(x\right)=\frac{4}{x^3}>0$ for $x=2$

$\therefore x=2$ is the point of minima

$\therefore$ Given function has local minima at $x=2$.

Ans: A