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

$$F(T)={\frac {1}{T+4-T}}\int _{T}^{T+4}P(t)\mathrm {d} t.$$

Can you proceed from here?