f(x)=2x^3-36x^2+162x-6

Question

small critical number? Large critical number?

Answer 1

I'm going to guess that the question is asking for the maximum and minimum of the cubic.

Simply find f'[x] = 0 and you will find 2 values for x. To find which is the max and min find f''[x]. and put in the two different values you got [say x1 and x2] and if f''[x1]>0 it's a minimum and if f''[x1]<0 it's a maximum. The same goes for x2.

Hope that helps