P(x) = 12x / (1-x)

Question

What are the critical points and where is P(x) increasing and decreasing?

Answer 1

critical points are where P'=0 or is undefined.

P' = 12/(x-1)^2
Since P' is always positive, P is always increasing

P'=0 never, so there are no min/max
P' is undefined at x=1, the vertical asymptote.

Enter this function at wolframalpha.com to see its graph and visualize what the above data indicate.