The graphs of y=3-x^2+x^3 and y=1+3x-2x^2+x^3 intersect in multiple points. Find the maximum difference between the y-coordinates of these intersection points.
Rearrange as
x^3 - x^2 + 3 = x^3 - 2x^2 + 3x +1
x^2 - 3x + 2 = 0 factor as
(x - 2) ( x -1) = 0
Setting both factors to 0 and solving for x produces x = 1 and x = 2
If x = 1 x^2 - 3x + 2 = 0
If x = 2 x^2 - 3x + 2 = 2
Max difference between y coordinates = 2 - 0 = 2
