A beginning calculus example

My older son is studying introductory calculus this year and so far (roughly the first two weeks) has been mostly learning about limits and derivative rules.

I wanted to try out a simple max / min problem just so he could get a peek at an application of some of the ideas he’s studying. I picked the standard problem about building a fence.

Here’s the first part -> what is the largest area enclosed by a rectangular fence if the perimeter is 40 feet?

Here’s the second part of the problem – now the rectangular fence has one side up against an existing wall. What’s the the maximum area now?