I may have overthought about problem 2.
Yes indeed. The solution you give in post #19 using simple calculus is much faster and simpler. Well done.
I noticed that P4 required the use of calculus? What, precisely, does that mean? If my approach doesn't qualify, it's fine.
There are various ways that can be used but I ask for the use of calculus as it is a fast and simple approach. Your first solution for question ##4## gets unnecessarily complex but the second is fine.