Science:Math Exam Resources/Courses/MATH101 B/April 2024/Question 18/Hint 2

We are tasked with finding the time $T$ for which the average population from $T$ to $T+4$ is as large as possible. This function is given by $$F(T)=\frac{1}{T+4-T}\underset{T}{\overset{T+4}{\int }}P(t)\mathrm{d}t.$$ Can you proceed from here?