I have this optimization problem which is mostly solved: "A box is to be made out of a 10 cm by 16 cm piece of cardboard. Squares of side length cm will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top." The volume must be maximized.
The objective function is and the crit point that gives a maximum is x = 2 (which equals ). The part I'm having trouble with is finding the domain which keeps both the length and volume positive.