Newton’s Method

Abstract

The search for solutions of the equation f(x) = 0 is ancient, and methods that can solve equations of the form ax2 + bx + c = 0 are several thousand years old. In the sixteenth century, Italian mathematicians discovered methods for solving third- and fourth-degree polynomials. However, it was shown in the early part of the nineteenth century that there is no general method for solving polynomials of degree five or higher. Consequently, methods for estimating solutions of equations as simple as polynomials are necessary. Isaac Newton developed such a method, which was later refined by Joseph Raphson, and which we now know as rNewton's method or the Newton-Raphson Method. Newton's method is easy to use and is often taught in first semester calculus since it only requires knowledge of the derivative.