Find the open interval(s) on which the curve given by the vector-valued function is smooth.

$\displaystyle r(t)=t^2i+t^3j$

If I follow the book correctly, I get the derivative which is $\displaystyle r'(t)=2ti+3t^2j$ and then after that I have no idea.

In the example problem it shows $\displaystyle r(t)=0i+0j$ and list some intervals, but I'm not sure what they're doing or what's going on.