Office File. Designs Unlimited plans to produce a one-component vertical file by bending t...

Office File. 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 ⨆ 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) Using the graph of the function shown below, determine how tall the file should be in order to maximize the volume that the file can hold.