# Maximum Volume of an Open Top Box

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 the folding up the flaps. Let x denote the length of each side of the square to be cut out.

1. Find the function V that represents the volume of the box in terms of x.

2. Graph this function and show the graph over the valid range of the variable x and show graph.

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

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#### Solution Summary

Maximum Volume of an Open-Top Box is investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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