Partial Derivatives : Extreme Values and Saddle Points (Modified) Partial Derivatives : Extreme Values and Saddle Points (Modified)

Abstract

One of the most useful applications for derivatives of a function of maximum and/or  minimum values. This application is also important for functions of two or more variables".The main ideas of finding critical points and Using derivatives tests are still valid.The tests of second derivatives for one variable give us the results for (a) Maximum and/or minimum points,(b) Points of inflection and (c) Test is inconclusive. while the second derivative for two variables give us the result fo : (a) Maximum and/or minimum points, (b) Saddle point and (c) Test is inconclusive. in this paper I had concentrated about the test of second derivative for the functions have two variables which depend on : fxx fyy fxy in such a way that there is a relationship between the discriminant (D) and fxx .modification will give relationship between D and fyy instead of fxx and the similarity between the point of infection in normal derivative and the saddle point in partial derivatives.