Question

find the critical numbers

Answer 1

@Directrix

Answer 2

I assume that the attachment describes what we are to do although I am somewhat leery of Wikipedia.

Take the first derivative of: 6x^3 - 288x - 3 to get y' = 18 x^2 - 288.

Setting that to zero will give the critical points.

18 x^2 - 288 = 0
x^2 - 16 = 0 --> Solve that for x. @SquirrelWingsMoose @Compassionate (Ambassador)

Crtical numbers and critical values are not necessarily the same so be sure you are answering the right question.