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Maximize the Volume of a Box: Exploring Polynomial Functions part of Spreadsheets Across the Curriculum:General Collection:Examples

In this Spreadsheet Across the Curriculum activity, students will create spreadsheets to find the maximum of a polynomial function. The module addresses the following optimization problem. Given a piece of cardboard 8 inches by 10 inches on a side, and letting x represent the length of a square cut out of each of the four corners of the cardboard sheet, what value of x produces the largest volume of open-top box made by folding up the cut-up cardboard? After exploring an applet available on the Internet, the students find x by creating a spreadsheet that evaluates and graphs the volume of the box as a polynomial function of x for many values of x. Then they find x again by differentiating the function, setting the derivative equal to zero, and creating a spreadsheet to solve the resulting quadratic equation in x.