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.

Algorithm. Let f be a differentiable function. Choose a point x1 near a root of f. Define recursively If the point x1 is chosen sufficiently close to the root then the xn's are successively better approximations of the root.

• Discussion [Using Flash]

• Example:
  • f(x) = xⁿ - a
    Discussion

• Drill problems on using Newton's Method.