Thread: Finding the local minima and maxima using the second derivative test

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!

Originally Posted by durrrr

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!

Stationary points occur where f'(x) = 0. If f''(x) < 0 at that point, then you have a local maximum. If f''(x) > 0 at that point, then you have a local minimum. If f''(x) = 0 at that point, the test is inconclusive.