This notebook contains the Mathematica commands from Chapter 14 of Introduction to Scientific Programming by Joseph L. Zachary.

(14.9)  We load the "Newton" package.

Needs["ISP`Newton`"]

(14.10).  This is a simple function with three roots.

example[x_] := x^3 - 9*x

(14.11)  We use "AnimateNewton" to animate the behavior of Newton's method as it makes four iterations toward finding a root, beginning with a guess of 1.3.

AnimateNewton[example, 1.3, 4, {-3.5, 3.5}]