Question

How do you find the critical points for `y = x^3 + 12x^2 + 6x + 8`?

Answer 1

Since `lim_(x->+-oo) f(x)=+-oo` there is no global maximum or minimum.

It has a local maximum at `x=-4-sqrt14` which is

`f(-4-sqrt14)=28(4+sqrt14)`

and it has local minimum at `x=-4+sqrt14` which is

`f(-4+sqrt14)=-28(sqrt14-4)`