On the function$\displaystyle \frac{x^2}{x^2+4} $

$\displaystyle y' = \frac{8x}{(x^2+4)^2}

y''=\frac{-24x^2+32}{(x^2+4)^3)}$

I thought the critical numbers would be taken from the 2nd derivative, but my teacher said from the 1st. Is it always like this? and how would i know to take it from the denominator or numerator?

Also into which equation would I plug the critical numbers into? The 1st deriv. or 2nd?