Question 573037
The maximum value of this function is {{{infinity}}}, since y grows without bounds with increasing x.
The minimum value is obtained when the derivative, dy/dx = 0:
dy/dx = 0 = (x-1)^3 + 3x(x-1)^2
Divide through be (x-1)^2 -> (x-1) + 3x = 0
4x - 1 = 0
x = 1/4
Putting this value in the original function gives y = (1/4)(-3/4)^3 = -27/256 ~ -0.105