A box is to be made out of a 8 cm by 20 cm piece of cardboard. Squares of side length x 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.
(a) Express the volume V of the box as a function of x.
(b) Give the domain of V in interval notation. (Use the fact that length and volume must be positive.)
(c) Find the length L, width W, and height H of the resulting box that maximizes the volume. (Assume that W?L).
(d) The maximum volume of the box is