An open box of maximum volume is to be made from a square piece of material 24 centimeters on a side by cutting equal squares from the corners and turning up the sides.

a) Write the volume V as a function of the length of the corner squares. What is the domain of the function?

b) Use a graphing utility to graph the volume function and approximate the dimensions of the box that yield a maximum volume.

c) Use the table feature of a graphing utility to verify your answer in part

b). The first two rows of the table are Height,x: 1 Length and Width: 24 - 2(1) Volume, V: 1[24 - 2(1)]² = 484 Height, x: 2 Length and Width: 24 - 2(2) Volume, V: 2[24 - 2(2)]² = 800.