find the minimum and maximum points of the curve y=x^4-4x^3+4x^2

Answer 1

min/max occur where y'=0
So, just solve

4x^3-12x^2+8x=0

So, which are min and which max?
Minimum if y" > 0 (concave up)
Maximum if y" < 0 (concave down)

So, take a look at y" = 4(3x^2-6x+2)