SOLUTION: The graphs of y=3-x^2+x^3 and y=1+x^2+x^3 intersect in multiple points. Find the maximum difference between the y-coordinates of these intersection points.

Algebra ->  Graphs -> SOLUTION: The graphs of y=3-x^2+x^3 and y=1+x^2+x^3 intersect in multiple points. Find the maximum difference between the y-coordinates of these intersection points.      Log On


   

Question 1029546: The graphs of y=3-x^2+x^3 and y=1+x^2+x^3 intersect in multiple points. Find the maximum difference between the y-coordinates of these intersection points.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
d%28x%29=3-x%5E2%2Bx%5E3-%281%2Bx%5E2%2Bx%5E3%29

d%28x%29=3-x%5E2%2Bx%5E3-1-x%5E2-x%5E3

d%28x%29=2-2x%5E2, a parabola with vertex as a maximum, something which is wanted. This maximum will be in the exact middle of the two zeros of d(x).

2-2x%5E2=0
1-x%5E2=0
1=x%5E2
x=0%2B-+1
The vertex x-coordinate is therefore at x=0.

Question is find the maximum difference between the two, or, evaluate d(x) for x=0.

d%280%29=2-x%5E2
d%280%29=2-0%5E2
highlight%28d%280%29=2%29