ABSTRACT
The graph of f :U ⊂ R2 → R is a subset of R3 and we will call it a surface. As we get to study graphs we will see that they have many of the features that we intuitively associate with surfaces and so our use of the word surface is not unreasonable. Since the graph is a subset of R3 a certain amount of ingenuity is required in order to obtain a faithful sketch and a number of standard approaches to this problem have been developed over the years. One method is to consider cross sections and by examining sufficiently many cross sections we may get ideas on where the maximum or minimum might be located.
