$$f'(x)= (x+1)^2(x-4)^5(x-2)^4 $$
For the critical points, I got $x = -1,2,$ and $4$. According to my professor's answer key, the interval is increasing on $(4, \infty)$ and decreasing on $(-\infty,4)$. I got increasing on $(-1,2)$ and $(4,\infty)$ and decreasing on $(-\infty,1)$ and $(2,4)$. Why are my answers wrong and why doesn't my professor consider the $-1$ and $2$ when determining where the function increases/decreases?