# Thread: Finding Critical Points of Functions

1. ## Finding Critical Points of Functions

Hello, and thanks in advance for the help.

I need to find the critical numbers of the function listed below. I understand that critical numbers mean one of two things, that the derivative at the point where x is critical is 0, or that the derivative does not exist.

It may simply be a simplification issue, but I'm having trouble solving for this derivative in a way that ti s manageable.

h(p) = (p-1)/(p^2+4)

Thanks again for the help!

2. $h(p)=\frac{p-1}{p^2+4}$

Just use the quotient rule..

$h'(p)=\frac{(p^2+4)-(p-1)2p}{(p^2+4)^2}$

$h'(p)=\frac{-p^2+2p+4}{(p^2+4)^2}$

use the quadratic formula and get the roots of the numerator and you will have your maximum or minimum values..Also we know there is no value of p that would set the numerator zero in the real numbers... so there is no asymptotes.