Designs Unlimited plans to produce a one-component vertical file by bending the long side of an 8-in. by 14-in. sheet of plastic along two lines to form a U shape.

(a) Express the volume of the file as a function of the height x, in inches, of the file.
(b) Find the domain of the function.
(c) Graph the function with a graphing calculator.
d) How tall should the file be in order to maximize the volume that the file can hold?

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14 in. 8 in.