Answer
$ f'(x)$ is positive for all $x>0$. This mean that $f(x)$ is increasing for $x>0$.
Work Step by Step
Given $$f(x)=2 x^{3}-10 x^{-1} \text { for } x>0$$
Since
$$ f'(x) = 6x^2-10x^{-2}$$
In the following figure, the green curve represents $f'(x)$. It is clear that $ f'(x)$ is positive for all $x>0$. This mean that $f(x)$ is increasing for $x>0$. ($f(x)$ is represented by the red curve).
