Newton's Method

An Interactive Applet powered by Sage and MathJax.

(By Kelsey Norman with HTML code from Prof. Gregory V. Bard)


\textrm{Newton's method: Given a a differentiable function } f \textrm{ and a ``seed" number } x_0,\\ \textrm{we generate a sequence of numbers } x_1, x_2, x_3, \ldots \textrm{ using the formula} \\ x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}, \qquad n = 0, 1, 2, \ldots. \\ \textrm{This sequence often converges (quickly) to a zero of } f.

Last modified on July 24th, 2017.