The first derivative of a function $~g~$ is given by $\qquad g^\prime(x)=\dfrac{x^2-6x+5}{x^2+5}\,$. Since $~g\,^\prime(1)=0~$ and $~g\,^\prime(5)=0\,$, both $~1~$ and $~5~$ are critical numbers of the function $~g$. The value $~g\,^{\prime\prime}(1)~$ is [[☃ dropdown 1]], which makes $~g(1)~$ [[☃ dropdown 2]]. The value $~g\,^{\prime\prime}(5)~$ is [[☃ dropdown 3]], which makes $~g(5)~$ [[☃ dropdown 4]].