The question is

> 
> $$\text{Let } f(r) = r^{1/3} + \frac 1r \text{ for } r>0$$
> a) Determine where the function $f$ is increasing or decreasing.
> 
> 
> b) Determine where the function $f$ is concave upward or downward.
> 
> 
> 

I've worked out

$$f'(r)= \frac 13r^{-2/3} -\frac 1{r^2}$$

but don't know how to work out the values of $r$.

What do I do next?