I recently completed a Calculus proficiency exam on tutor.com. Here is a question they asked me:

An open box is to be made from a 20 inch square piece of cardboard by cutting four equal square pieces from each corner and turning up the sides. What is the side length of the pieces that should be cut out so that the box will have maximum volume?

This questioncanbe done, using partial derivatives, but this solution (that the cardboard is a square with sides $\displaystyle \sqrt{20}$ inches long) was not listed as one of the possible answers. Not to mention the exam was supposed to use Calc I techniques, of which I doubt partial derivatives are included.

Is there any way to generate a solution here without resorting to partial derivatives? (I finally answered the question by process of elimination: only one answer listed was physically possible.)

-Dan