differential equation problem(i think)

I didn't know what to title this post

Suppose that the population of bacteria P(t) changes according to

P(t) = 4000(1 + (2t/1+t^2)) where t is given in hours and t is eual to or greater than 0

a) when does the population reach the maximum number?

b) What is the maximum population?

I been looking through this from a previous test and trying to figure out how I got the answer...According to my professor I did some things wrong and got marked down 3 out of 10 points, but I still ended up with the right answer.