Question

$f\left(x\right)=xlnx-x$ is an increasing function in the interval

• A. $(0,\infty )$
• B. (0, 1) U (1,2)
• C. $(1,\infty )$
• D. $(-\infty ,\infty )$

Answer 1

The correct option is C $(1,\infty )$

$f\left(x\right)=x\ln x-x$
Clearly, f(x) is defined for x>0
$f^{\prime }\left(x\right)=\ln x$
For f(x) to be increasing,
$f^{\prime }\left(x\right)>0$
$\Rightarrow \ln x>0$
$\Rightarrow x>1$
$\Rightarrow x\in (1,\infty )$