What is the smallest possible value of their sum? The product of two positive numbers is 36. What is the smallest possible value of their sum?
so far I got
$$xy=36$$
$$y=\frac{36}{x}$$

Note: there are many ways you can show this but i am assuming from your tag you need an answer via derivatives here it goes
let $m=x+y=x+\frac{36}x=x+36x^{-1}$
then $m'=1-36x^{-2}$
to have a minimum value of $m$ let $m'=0$
$1-36x^{-2}=0$
$36=x^2$
so $x=6$ and $y=6$
