Some examples of applying quadratic forms to find constrained extrema of functions of several variables

Abstract

In this paper, we present three main contents, including. Basic concepts of quadratic forms, including: definition of quadratic forms, positive definite forms, negative definite forms, indefinite forms, and canonical quadratic forms. Concepts related to extrema of multivariable functions, such as: maximum, minimum on the domain, conditional extrema, along with necessary and sufficient conditions to determine extrema. Some specific illustrative examples, showing how to apply quadratic forms in finding conditional extrema of multivariable functions.