An open box of maximum volume is to be made from a square piece of material 24 centimeters on a side by cutting equal squares from the corners and turning up the sides (see figure).
(a) Write the volume V as a function of x, the length of the corner squares. What is the domain of the function?
(b) Use a graphing utility to graph the volume function and approximate the dimensions of the box that yield a maximum volume.
(c) Use the table feature of the graphing utility to verify your answer in part (b).
|Height, x||Length and Width||Volume, V|
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