The function f(x)=x 2 +2 x has a local minima at x equal to - Vidyadip

Question

The function $f(x)=\frac{x}{2}+\frac{2}{x}$ has a local minima at $x$ equal to

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Answer

Given, $f(x)=\frac{x}{2}+\frac{2}{x} \Rightarrow f^{\prime}(x)=\frac{1}{2}-\frac{2}{x^2}$
For extremes $f^{\prime}(x)=0 \Rightarrow \frac{1}{2}-\frac{2}{x^2}=0 \Rightarrow x= \pm 2$
$f^{\prime \prime}(x)=\frac{4}{x^3}>0$ for $x=2$
$\therefore \quad x=2$ is the point of local minima.

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