Hi, stuck on this question, I'm under a strict deadline so I'm moving through my material really quickly and probably leaving a lot of gaps in my knowledge.

f(x)=12 + 2x^3 - 4x^4

Questions are:

Use the second derivative test to identify the local maxima and minima.

Locate the inflection points of the graph of the function.

I understand that f'(x) = 6x^2 - 16x^3 and f''(x) = 4 - 48x^2 but I am not sure where to go from here.

Please help!