Objectives: In this tutorial, we examine Newton's Method and see the
geometry underlying the derivation of the algorithm. We also look at a few examples that illustrate the method.
After working through these materials, the student should be able
to understand graphically the derivation of Newton's Method,
to apply Newton's Method to find the roots of a function.
Modules:
Algorithm. Let f be a differentiable function. Choose
a point x_{1} near a root of f. Define recursively
If the point x_{1} is chosen sufficiently close to the root then the x_{n}'s
are successively better approximations of the root.