I am trying to test my understanding of the definition of smooth curves, as given to me in a text: a smooth curve has a bounded, continuous derivative on the interior of its parametric interval.

So, if I let C= $\displaystyle \left( t, \frac{-1}{t^2} \right)$, for $\displaystyle t \ge 0$ , then C' is unbounded. So C is not a smooth curve?