$\displaystyle F(x) = \frac{p-4}{p^2+2}$

f(x) = p-4

f'(x) = -4

g(x) = $\displaystyle p^2 + 2$

g'(x) = 2p

$\displaystyle F'(x) = \frac{f'(x)g(x)-f(x)g'(x)}{g(x)^2}$

$\displaystyle F'(x)= \frac{-6p^2+8p-8}{(p^2+2)^2}

$

I understand that a critical number is where F'(x) is either c or DNE.

But as far as I can tell, neither the bottom nor the top can be equal to 0, which I think neglects both cases.