The maximum value of (\frac{log\_ex}{x}), if x > 0 is | Mathematics | SolveeIt

The maximum value of $\frac{log_ex}{x}$ , if x > 0 is

$e$

$1$

$\frac{1}{e}$

$- \frac{1}{e}$

Answer

$\frac{1}{e}$

Explanation

$(y = \frac{log_e \ x}{x})$
$? \left(\frac{dy}{dx}=\frac{1 - log_e x}{x^2}\right)$

For maxima, $dy/dx = 0$
$? 1 - log_e x = 0$
$? x = e$
$dy/dx$ changes sign from positive to negative at $x = e$
$? y_{\text{max}} = 1/e$

Mathematics Question on Maxima and Minima