Question

$f\left(x\right)=x+1/x$, $x\ne 0$ is monotonic increasing when -

• A. $|x|<1$
• B. $|x|>1$
• C. $|x|<2$
• D. $|x|>2$

Answer 1

Answer: (B)

$|x|>1$

$f\left(x\right)=x+\frac{1}{x}$
$f^{\prime }\left(x\right)=1-\frac{1}{x^2}$
Now
$f^{\prime }\left(x\right)>0$
Gives
$1>\frac{1}{x^2}$
Or
$x^2>1$
Or
$|x|>1$ ...for $f\left(x\right)$ to be an increasing function,
Or
$xϵ(-\infty ,-1)\cup (1,\infty )$