# Will you compare coefficients?

Calculus Level 5

\begin{align} C_1: f\left( x \right) &=x^6+Ax^5+Bx^4+Cx^3+Dx^2+Ex+F \\ C_2: g\left( x \right) &=Px+Q \end{align}

Consider the curves $$C_1$$ and $$C_2$$ where $$A,B,C,D,E,F,P,Q \in \mathbb{R}$$.

Now it is given that $$f\left( x \right)$$ touches $$g\left( x \right)$$ at $$x=1,2,3$$. Let $$\mathcal{A}$$ be the area bounded between the two curves $$C_1$$ and $$C_2$$.

If $$\mathcal{A}$$ can be expressed in the form $$\frac{m}{n}$$, find $$m+n$$.

Details And Assumptions

• $$m,n$$ are co-prime integers.
×