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Maximizing the Volume of an Open-Top Box

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An open top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and then folding up the flaps. Let x denote the length of each side of the square to be cut out.

Find the function V that represents the volume of the box in terms of x. Show and explain the answer, and also graph this function.

Using the graph what is the value of x that will produce the maximum volume?

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Solution Preview

After cutting four squares, the length that is left is 8-2x feet and the width that is ...

Solution Summary

This solution provides a detailed response, which illustrates how to calculate the volume of an open-top box. The solution is easy to follow and includes a graph, which is attached in an accompanying Word document as part of this solution.