MCQ
The function $f ( x )=\frac{x}{2}+\frac{2}{x}$ has a local minimum at
  • A
    $x=-1$
  • B
    $x=-2$
  • C
    $x=2$
  • D
    $x=1$

Answer

(c) $x=2$
Explanation: $f ( x )=\frac{x}{2}+\frac{2}{x} \Rightarrow f ^{\prime}( x )=\frac{1}{2}+\frac{2}{x^2}$ and $f ^{\prime \prime}( x )=\frac{4}{x^3}$
Now, $f^{\prime}(x)=0 \Rightarrow x^2=4 \Rightarrow x= \pm 2$
$
\because f^{\prime \prime}(2)=\frac{4}{2^3}=\frac{1}{2}>0
$
$\Rightarrow f(x)$ has a local minimum at $x=2$

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