Maximizing
or Minimizing Polynomials Using Algebraic Inequalities
Tilak de
Alwis
talwis@selu.edu
Department of Mathematics
Southeastern Louisiana University
United States
Abstract
In mathematics, several methods can be used to maximize or minimize
polynomials and other types of functions. One such method uses techniques
in calculus, such as the derivatives. However, there are several
types of functions which can be maximized or minimized without resorting
to methods of calculus. For example, quadratic functions can be
maximized or minimized using the method of completing the square.
In this paper, we will discover a brandnew method for optimizing
certain types of functions. The new method that we will describe
is based on a famous inequality in algebra, known as the Inequality
of the Means. The proposed method can be considered as a surprising
application of the above mentioned inequality. One can check the
results obtained from this method by using calculusbased methods,
or by using computer algebra systems such as Mathematica.
