(a) (12 分) Sketch the graph of the function by finding all asymptotes, interval of increasing and decreasing, and interval of concavity.

(3) To create an open box from a square piece of cardboard, we can cut out identical squares from each corner and then fold up the resulting flaps. If the cardboard measures 10 inches on each side, determine the dimensions of the box that will yield the maximum volume. Note: Points will be awarded only if calculus is used in the solution.