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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

Answer 1

http://www.twiddla.com/solved

Answer 2

so is it solved ?

Answer 3

nope, they are working on it there.

Answer 4

f(x) has to be a quadratic eqn

Answer 5

yeap: "Let f(x) be a quadratic function such that f(0) = -8"

Answer 6

Ok, try defactorizing your f(x), then as the function has to be a quadratic eqn (degree 2)....just equate the coefficients of higher degree terms to 0. Then you might get the values of your variables!

Answer 7

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. and we know what A is.

Answer 8

f'(0) = b

We have to find the value for b, and we're done

Answer 9

done?

Answer 10

plug A back into the equation then take the derivative. It will look like this f'(x) = (A(x+7)^5)' + x(...) + x(...) + x(...) .... so you really only need to worry about the first term since x is 0 everything will disapear and f'(0) = 5A* 7^4 = -40/7

Answer 11

I'm so stupid, it would be 5*7^4*A

Answer 12

yes right!

Answer 13

Yeah, that's it.

Answer 14

If f'(0) =b, it should be a numerical value

Answer 15

Yup, its -40/7

Answer 16

Oh, nice

Answer 17

glad I could help.

Answer 18

Thanks everyone, it's done. The answer was really small like .00 sth. :)