I have following function 

$$f(x)=\begin{cases}
x^2\cos\left(\frac1x\right) &\text{if }x\neq0\\
0 &\text{if }x=0
\end{cases}$$

How can I prove that this function in every area of zero has positive and negative values? I thought about finding appropriate sequences, but I can't come up with idea which exactly. Could someone clue me in on good solution?