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Math 125-103 Fall 2012 Quiz 2 A box with an open top is to be constructed from a rectangular piece of cardboard that is 14 inches by 22 inches by cutting out equal squares of side length x from each corner and folding up the sides as indicated. Express the volume as a function of x. x Carter x x x x 14” x 22” Solution. The edge lengths of the open box are x, 14 − 2x, and 22 − 2x. Therefore the volume is V = x(14 − 2x)(22 − 2x). For the purposes of future problems, it is not wise to multiply out the solution. V = 4x3 − 72x2 − 308x. 1 x x