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Find Domain, Graph, Height, Minimum Surface Area of a Box

Consider an open-top box with a square base and a volume of 108 cubic inches. Let x be the length of a side of the base.

a) Calculate the height h as a function of x. Is this function even, odd, or neither?

b) What is the domain of the function above? (Note that there may be physical and/or mathematical restrictions.)

c) Given that the minimum possible surface area of the box is 108 square inches, find the expression expressing the length of the side of the base vs. surface area, and draw a reasonably accurate graph of that expression with length of the base x on the horizontal axis and surface area on the vertical axis.

d) Is the above expression a function?

Solution Summary

Domain, Graph, Height, Minimum Surface Area of a Box are found Given its Volume. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.