Question

$f\left(x\right)=|x1nx|:x\in (0,1)$, then $f\left(x\right)$ has maximum value $=?$

• A. e
• B. $\frac{1}{e}$
• C. $1$
• D. None of these

Answer 1

The correct option is B $\frac{1}{e}$

$f\left(x\right)=|r\ln x|$

$f^{\prime }\left(x\right)=\frac{|r\ln x|}{x\ln x}(\ln +1)=0$

$\Rightarrow \ln x=-1$

$\Rightarrow x=e^{-1}\Rightarrow x=\frac{1}{e}$