Advanced Calculus  Fundamentals of Mathematics

Advanced Calculus Fundamentals of Mathematics

Vector calculus is an essential mathematical tool for performing mathematical analysis of physical and natural phenomena. It is employed in advanced applications in the field of engineering and ...
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Critical Points

Pp. 46-63 (18)

Carlos Polanco

Abstract

This chapter focuses on the identification of the maximum, minimum, or saddle points located in the domain of the real-valued function in a graph of a function. The first part of this chapter focuses on the open set domain of a function and the second part on the closed set domain. The characterization of these points called critical points" is resolved with the Hessian matrix and the Bordered Hessian matrix. Finally, we will review the Implicit Function Theorem.

Keywords:

Bordered Hessian matrix, Closed set, Critical points, Hessian matrix, Implicit function theorem, Inverse function theorem, Inflection value, Inverse function, Maximum points, Maximum value, Minimum points, Minimum value, Open set, Saddle point, Second order partial derivative.

Affiliation:

Department of Mathematics Faculty of Sciences Universidad Nacional Autónoma de México México City México.