Concept explainers
25. Constructing an Open Box An open box with a square base is to be made from a square piece of cardboard 24 inches on a side by cutting out a square from each corner and turning up the sides. See the figure.
(a) Express the volume V of the box as a function of the length x of the side of the square cut from each comer.
(b) What is the volume if a 3-inch square is cut out?
(c) What is the volume if a 10-inch square is cut out?
(d) Graph . For what value of x is V largest?

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