1. The problem statement, all variables and given/known data 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) 2. Relevant 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. 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.