Question

find maxima and minima of y=log x/x

Answer 1

$y=\frac{Log\ x}{x},\ \ 0 < x < \infty\\\\\frac{d}{dx}(\frac{u}{v})=\frac{vu'-uv'}{v^2}\\\\\frac{dy}{dx}=\frac{x*\frac{1}{x}-(Log\ x)*1}{x^2}=\frac{1-Log\ x}{x^2}\\\\y'=0,\ \ for\ \ Log\ x=1,\ \ =>x=e$

y' > 0 for  x < e
y' = 0 for x = e
y' < 0 for x > e

The Log x / x  has a local maximum at e.  There are no local minima.