#### Answer

The critical numbers are $p=1\pm \sqrt 5$

#### Work Step by Step

Find the critical values of this function $h(p)=\frac{p-1}{p^2+4}$
Differentiate and set the derivative $=0$
$h'(p) = \frac{p^2+4-2p(p-1)}{(p^2+4)^2}$
Critical numbers exist where the derivative $= 0$. The derivative $= 0$ when the numerator $= 0$
$0=p^2+4-2p^2+2p$
$0=-p^2+2p+4$
Solve for $p$ with the quadratic formula
$p=1\pm \sqrt 5$