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.
Related Books
Boundary Element Methods for Heat Transfer with Phase Change Problems: Theory and Application
Advanced Numerical Methods for Complex Environmental Models: Needs and Availability
An Introduction to Sobolev Spaces
An Introduction to Trigonometry and its Applications
Analysis and Optimal Control of Phase-Field Transition System: Fractional Steps Methods
Applied Computational Mathematics in Social Sciences
Calculus: The Logical Extension of Arithmetic
Complex Analyses in Engineering, Science and Technology
Convergence Theorems for Lattice Group-Valued Measures
