The functioin f ( x ) = x 2 + 2 x has a local minimum at X= .....… - Vidyadip

MCQ

The functioin $f\left( x \right) = \frac{x}{2} + \frac{2}{x}$ has a local minimum at $X=$ ........

A
$ - 2$
B
$ 0$
C
$ 1$
✓
$ 2$

✓

Answer

Correct option: D.

$ 2$

d
$f(x)=\frac{x}{2}+\frac{2}{x} \Rightarrow f^{\prime}(x)=\frac{1}{2}-\frac{2}{x^{2}}=0$

$\Rightarrow x^{2}=4$ or $x=2,-2 ; \quad f^{\prime \prime}(x)=\frac{4}{x^{3}}$

$\left.f^{\prime \prime}(x)\right]_{x-2}=+v e \Rightarrow f(x)$

has local min at $x=2$

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