Maximum Perimeter

https://www.desmos.com/calculator/sav3mbb1gq

Below is the graph of the parabola.

Consider the family of all rectangles with base along the x-axis inscribed underneath the parabola. Three members of this family are sketched in the diagram.

The problem is to find the rectangle with the largest perimeter.

This looks like a calculus problem, except in grade 12 it is typically the area of the rectangle that is maximized. In replacing area with perimeter, we bring this problem into the grade 10 domain. We think that is a good problem because right way the students are faced with the task of find a good parameter to work with.