I need to find the absolute maximum and minimum of the function below on the interval [0,4]

g(x) = x / x^2 + 4

I know that i need to find g' which i think is

g'(x) =(x^2 + 4)1 - x(2x)

(x^2 + 4)^2

g'(x) =4 - x^2

(x^2 - 4)^2

Am I correct so far? Do I need to do g'' or should I factor out and find the critical values?