القيمة العظمى والقيمة الصغرى للدالة التربيعية جبريًا

Abstract

This paper aims at presenting a simple method to find the extremum (extreme
values) of a two-variable square function. We introduce a generalized method of
finding the extremum of a one-variable square function at the outset. The proposed
method relies on square completion only. Therefore, it is a pure algebraic method.
The method can be used to teach advanced junior-high school pupils. One salient

advantage of this solution is that it helps us arrive at the partial derivatives of the
determinant of the Hessian (see [1]). Our proposal handles very well the case in
which the determinant of the Hessian equals zero. We get a necessary and
sufficient condition to determine whether the critical point is an extremum in this
case.