d) If D = 0, then no conclusion can be drawn. c) If D < 0, then f has a saddle point at (a,b). The following example illustrates a … Suppose z=f(x_1,x_2,...,x_n). b) If D > 0 and f xx (a,b) < 0, then f has a relative maximum at (a,b). In this paper we work with functions of two variables and introduce the concept of constrained extrema for this kind of functions. 3.Evaluate f(x;y) at the found points. Maxima and Minima for Functions of More than 2 Variables The notion of extreme points can be extended to functions of more than 2 variables. In Sections 2.5 and 2.6 we were concerned with finding maxima and minima of functions without any constraints on the variables (other than being in the domain of the function). Extrema for a function of four variables with two auxiliary equations. Well Lagrange multiplier will help you, but since you have 2 equations, you can easily to reduce the function to a one variable, which is easily to maximize or minimize. Examples with Detailed Solutions We now present several examples with detailed solutions on how to locate relative minima, maxima and saddle points of functions of two variables. What would we do if there were constraints on the variables? These extreme values are not necessa- Suppose we wish to find the maxima or minima of a function u = F(x, y, z, t) with the side conditions … How to nd the absolute extrema of a continuous function of two variables on a closed and bounded set R? The largest of these values is When too many critical points are found, the use of a table is very … That is, we calcu-late the maximum and minumum value of a function of two variables under some extra conditions (constraints). 1.Find the critical points of fthat lie in the interior of R. 2.Find all the boundary points at which the absolute extrema can occur.