ABSTRACT
In this chapter, the authors develop criteria for finding the points at which a function of several variables takes on its maximum or minimum. In many applications of mathematics, one wishes to maximize or minimize some function. In economics, for example, it is usual to try to maximize profit or minimize cost. Finding the extreme values of a function of one variable is one of the applications of elementary calculus. In this case, of course, there are only two boundary points, while for a function of several variables there are infinitely many. As a result, we need to develop a special procedure for dealing with maxima and minima at boundary points. This procedure, called the method of Lagrange multipliers.
