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

The function $f(x)=\frac{x}{2}+\frac{2}{x}$ has a local minimum at
  1. x = 2
  2. x = −2
  3. x = 0
  4. x = 1

Solution

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

Asked in: JEE Main 2006

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