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bur7ama1989
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Homework Statement
I am working on a Calculus I project and the last question has me stunned. I would really appreciate some assistance in this. Maybe a push in the right direction.
So here is the problem word for word. There is also an attachment containing a picture of the problem.
Suppose that the cubic function "y = a(x^3) + b(x^2) + cx + d" and the parabola "y = k(x^2) + mx + n" intersect at "x=A" and "x=B" and that the curves are tangent at B (that is, the derivatives are equal at "x=B").
Show that the area between the curves is equal to
Area = ((absolute(a))/12)((B-A)^4)
Homework Equations
I made the first equation into f(x):
f(x)=a(x^3)+b(x^2)+cx+d
and the second equation into g(x):
g(x)=k(x^2)+mx+n
I found the derivatives:
f'(x)=3a(x^2)+2bx+c
g'(x)=2kx+m
I equated them
3a(x^2)+2bx+c=2kx+m
I now have a system of three equations with 9 variables and the answer shows only 3.
The Attempt at a Solution
I played with these equations until my neck hurt.
1)
f(A)=g(A)
2)
g(B)=g(B)
After those two steps I began solving for one variable at a time and trying to remove them from the question. Needless to say I have failed. Please help me out.