As shown in the figure below, square corners of a thin piece of cardboard measuring 6 in. by 6 in. are cut out so that the sides can be folded up to make a small box without a lid.
What dimensions of the box will maximize its volume?
In your work, you should clearly identify the quantity to be maximized and then the function expressing it in terms of a single variable. State the domain of the function and show all the work needed to find and verify the maximum.