Did I tell you I was gonna become a minimalist? Once again

If you're gonna maintain a minima list, you should take into account the maxima. You can find both by solving the equation f'(x)=0 where differentiable. These can tested solving for f''(x) at the critical points: if f''(x) <0 it is a maximum if f''(x)>0 it goes on the minima list.