Question

Find local maximum value of function (x)$=\frac{\ln x}{x}$

• A. $\frac{1}{e}$
• B. $\frac{-1}{e}$
• C. $\frac{2}{e^2}$
• D. None of these

Answer 1

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

$f\left(x\right)=\frac{\ln \left(x\right)}{x}$
$f^{\prime }\left(x\right)$$=\frac{1-\ln \left(x\right)}{x^2}$$=0$
Or
$\ln \left(x\right)=1$
$x=e$ ...(i)
Now
$f\left(e\right)$$=\frac{1}{e}$.
Hence local maximum value of $f\left(x\right)$ is $\frac{1}{e}$.