The min of $x + k/x$ $f(x) = x + \dfrac{k}{x} $ ($k > 0$ and $x > 0$)
given that the k is a constant, how do I solve the x that makes f(x) minimum?

To avoid differentiating, notice that
$$x+\frac{k}{x}=\bigg(\sqrt{x}-\sqrt{\frac{k}{x}}\bigg)^2+2\sqrt{k}$$
and that $\sqrt{x}=\sqrt{k/x}$ when $x=\sqrt{k}$.
(Note that we can use $\sqrt{x}$, since it is given that $x\gt 0$)
