Smooth functions

Hi,

there is a function in form x(t), y(t). How to check for what ranges of t function's curve is ragged and when it's smooth?

>>4 by ragged or smooth I mean common sense of them, e.g. 100*sin(x) is smooth, 0.5*sin(x) is ragged, abs(x) is ragged near to x=0, otherwise it's smooth. I'm not sure how to translate common sense of those terms into math.
10/10 I raged more than once.