Volume of a Box A piece of cardboard is 3 times as long as it is wide. Equal-sized squares measuring 4 inches on each side are to be cut from the corners of the piece of cardboard, and the flaps will be folded up to form a box with an open top.
(a) Determine a function V that describes the volume of the box as a function of x, where x is the original width in inches.
(b) What should be the original dimensions of the piece of cardboard if the box is to have a volume of 2496 cubic inches? Solve this problem analytically.
(c) Support the answer in part (b) graphically.
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