You want to make an open box from a rectangular piece of material, 15 centimeters by 9 centimeters, by cutting equal squares from the corners and turning up the sides.
(a) Let x represent the side length of each of the squares removed. Draw a diagram showing the squares removed from the original piece of material and the resulting dimensions of the open box.
(b) Use the diagram to write the volume V of the box as a function of x. Determine the domain of the function.
(c) Sketch the graph of the function and approximate the dimensions of the box that yield a maximum volume.
(d) Find values of x such that V = 56. Which of these values is a physical impossibility in the construction of the box? Explain.