Science:Math Exam Resources/Courses/MATH102/December 2017/Question 10 (d)/Solution 1

By the Hint, for Patch 1 a secant line has maximum slope just a bit before ${\textstyle f_{1}}$ reaches its maximum. An approximate optimal time is ${\textstyle t=50}$.

For Patch 2, the slope is largest when ${\textstyle t=100}$. Hence the optimal time is ${\textstyle t=100}$.

To summarize, the optimal time (indicated by the red dots) for Patches 1 and 2 are as follows.