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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.

 Apr 22, 2022
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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

 

 

cool cool cool

 Apr 23, 2022

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