When a question states that "how smooth is $f~$" what should I do? For example how can we apply it in this question :
Consider the function $f: R\rightarrow R$ defined by
$ f(x) = \begin{cases}x^{2}\sin(1/x^2 ) & ~~\text {if}~~ x≠0;\\ 0 & ~~\text{if}~~ x=0; \end{cases}$
How smooth is $f$ ? What should I do? Is green theorem related to these kind of questions?