This is what I think it is:
So if the population is increasing and I'm taking away , how much can I take away to just balance the amount being added to the population? That means, I'm taking away just enough so that the population is not changing at all. That means the rate . Solving for that, I get the rate is unchanging when . Now, what is the largest can be? Surely, we don't wish imaginary numbers, so how large can be before that expression in the square root becomes zero?