Let f(x) be a quadratic function such that f(0) = -8 and integral of [f(x) /((x^2)(x+7)^5) dx is a rational function.

Determine the value of f'(0).

I got f(x) = A(x+7)^5+D(x+7)^3(x^2) + E(x+7)^2(x^2)+F(x+7)(x^2)+Gx^2

since f(0) = -8, A = -8/(7)^5

Now I am stuck

Question

Let f(x) be a quadratic function such that f(0) = -8 and integral of [f(x) /((x^2)(x+7)^5) dx is a rational function.

Determine the value of f'(0).

I got f(x) = A(x+7)^5+D(x+7)^3(x^2) + E(x+7)^2(x^2)+F(x+7)(x^2)+Gx^2

since f(0) = -8, A = -8/(7)^5

Now I am stuck

anonymous · Answer

No one?

anonymous · Answer

If you derive the function you have, and look for f'(0), all of the other variables (D, E, etc.) wont matter, because when you derive it they have x^1 or greater (since x is now 0). So the only term that remains is the derivative of the second to last term of the expanded A(x+7)^5. The last term of that expansion goes away because it was a constant that got derived.