Question

Show that the functions given by $f\left(x\right)=\frac{\log x}{x}$ has maximum at $x=e$.

Answer 1

Given, $f\left(x\right)=\frac{\log x}{x}$

$f^{{}^{\prime }}\left(x\right)=\frac{1-\log x}{x^2}$

Putting this equal to zero, we get

$x=e$

Which means the given function will have maximum at $x=e$