Solved: Numerical and Graphical Analysis An open box is to

Chapter 2, Problem 2.2.91

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Numerical and Graphical Analysis An open box is to be made from a square piece of material 36 centimeters on a side by cutting equal squares with sides of length x from the corners and turning up the sides (see figure). (a) Verify that the volume of the box is given by the function (b) Determine the domain of the function V. (c) Use the table feature of a graphing utility to create a table that shows various box heights x and the corresponding volumes V. Use the table to estimate a range of dimensions within which the maximum volume is produced. (d) Use a graphing utility to graph and use the range of dimensions from part (c) to find the value for which is maximum.