I have no clue how to even begin this problem..

Okay, so the function:

satisfies this logistic model:

For which value of t is P'(t) maximum? What is the value of P for this t?

For this problem, this function is used to model the spread of a disease where P is the proportion of people infected. Each person infects, on average, k other people.

Now, I understand that the first function is the integral of the second. But I'm so confused when it comes to understanding what exactly I need to derive. Can someone please help me walk through this?