# Thread: Rational Functions ~ Calculus

1. So here is my problem i am suppose to graph f(x)= (20x^2-20)/(x^3+x^2) but i am not sure if i am doing it correctly. I got a vertical asymptote at x=0 and a horizontal asymptote at y=0. Now, I believe these to be right, but once i get to the first derivative (to find local extrema) I become bewildered. I am not sure if i am doing it right and since its crucial to be done right in order to find the second derivative (concavity and point of inflection); therefore i need much appreciated assistance. I got f1(x)= (-39x^2+40x)/(x^2)^2 . If anyone can confirm anything or point out errors it would be greatly appreciated.  2.

3. f(x) = (2x^2-20)/(x^3+x^2)

The derivate to this is:

f'(x) = (4x*(x^3+x^2)-(2x^2-20)(3x^2+2x))/((x^3+x^2)^2)
Didn't have time to shorten it though...

That would leed you the way   4. Ok so i got f'(x) = (-20x^4 + 60x^2 + 40x)/(x^3 + x^2)^2 can i assume that there are no local extremas? So i now have found f''(x) to be
f''(x)= (-20x^6 + 80x^5 - 60x^4 - 80x^3 - 160x^2)/(x^3 + x^2)^4
How correct am I? I need this info in order to graph the function...i need f''(x) to be correct in order to find concavity and point of inflection.  Bookmarks
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