Volume of a Box. From a 12-cm by 12-cm piece of cardboard, square corners are cut out so t...

Volume of a Box. From a 12-cm by 12-cm piece of cardboard, square corners are cut out so that the sides can be folded up to make a box.

a) Express the volume of the box as a function of the side x, in centimeters, of a cut-out square.

b) Find the domain of the function.

c) Using the graph of the function shown below, determine the dimensions that yield the maximum volume.