Maximizing or Minimizing Polynomials Using Algebraic Inequalities

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 brand-new 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 calculus-based methods, or by using computer algebra systems such as Mathematica.