Find the dimensions of the closed rectangular box with square base and volume 8000 cubic centimeters that can be constructed with the least amount of material by the following steps.
(1) Let x be the length of each edge of the base and y the height. What equation do they satisfy?
(2) Find out the area function f(x).
(3) Find the critical points of f(x).
(4) Discuss the increasing and decreasing property of f(x).
(5) Find the dimensions asked in the problem by the First Derivative Test.