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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.

 Jun 23, 2022
 #1
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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

 

 

cool cool cool

 Jun 23, 2022

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