The graphs of y = 3 - x + x^3 and y = 2 + x^2 + x^3 intersect in multiple points. Find the maximum difference between the y-coordinates of these intersection points.
+128475 See the graph here : https://www.desmos.com/calculator/gfuwb9pkj7
The intersection points are somewhat interesting = ( ≈.618, ≈ 2.618) and ( ≈ -1.618 , ≈ .382)
These points are actually ( Phi ^(-1) , Phi^2) and ( -Phi , Phi^(-2) )
The actual difference in the y values =
Phi^2 - Phi^(-2) =
(Phi + 1) - ( 1 -phi) =
Phi + phi ≈ 2.236
