Solving a word problem by finding a local extremum of a polynomial function

# Solving a word problem by finding a local extremum of a polynomial function

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Solving a word problem by finding a local extremum of a polynomial function A box with a hinged lid is to be made out of a rectangular piece of cardboard that measures inches by inches. Six squares will be cut from the cardboard: one square will be cut from each of the corners, and one square will be cut from the middle of each of the -inch sides (see Figure 1). The remaining cardboard will be folded to form the box and its lid (see Figure 2). Letting represent the side-lengths (in inches) of the squares, use the ALEKS graphing calculator to find the value of that maximizes the volume enclosed by this box. Then give the maximum volume. Round your responses to two decimal places. After cutting squares of side length from a side with length , the cardboard remaining on this side will have length . Thus, the pieces of cardboard left will each have length . Furthermore, cutting squares of side length from a side with length yields a piece of cardboard with length (see Figure 3). Therefore, the box formed from this cut rectangle will have

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Solving a word problem by finding a local extremum of a polynomial function

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