Find the non-zero critical points of $f$ and the signs of the values of $f$ at these non zero critical points.
Determine the behaviour of $f$ between the non zero critical points and the types of non-zero critical points
I understand that this function is oscillating in between $(-0.3183, 0)$ and $(0.3183,0)$ and have also proven that $f'(0) = 0$ using the formal derivative definition as well as the squeeze theorem.
I also found $f'(x) = 2x\sin \frac 1x - \cos \frac 1x$ but am having difficulty finding a way to list and classify the critical points in a general manner.
Any help is appreciated!