Question: You construct an open box from a square piece of material, 36inches on a side, by cutting equal squares with sides of length x from

You construct an open box from a square piece of material, 36inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure).

(a) Write a function V that represents the volume of the box.
(b) Determine the domain of the function V.
(c) Use a graphing utility to construct a table that shows the box heights x and the corresponding volumes V(x). Use the table to estimate the dimensions that produce a maximum volume.
(d) Use the graphing utility to graph V and use the graph to estimate the value of x for which V(x) is a maximum. Compare your result with that of part (c).

A-36 2x A I

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