The function f(x)=x+4 x has - Vidyadip

MCQ

The function $f(x)=x+\frac{4}{x}$ has

A
a local maxima at $x=2$ and local minima at $x=-2$
✓
local minima at $x=2$, and local maxima at $x=-2$
C
absolute maxima at $x=2$ and absolute minima at $x=-2$
D
absolute minima at $x=2$ and absolute maxima at $x=-2$

✓

Answer

Correct option: B.

local minima at $x=2$, and local maxima at $x=-2$

(b) : Given, $f(x)=x+\frac{4}{x}$
$
f^{\prime}(x)=1-\frac{4}{x^2} \quad \therefore f^{\prime}(x)=0 \Rightarrow x= \pm 2
$
and $f^{\prime \prime}(x)=\frac{8}{x^3}$ which is $>0$ for $x=2$ and $<0$ for $x=-2$
$\therefore f(x)$ has local minima at $x=2$ and local maxima at $x=-2$.

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