If we carefully apply Newton's Method to solve f(x) = 0, it will almost always produce the desired solution. What do we mean by carefully? To get a feeling for what we mean, in each of the following examples try to predict the sequence of estimates produced when Newton's Method is applied with the given x₀.

Copyright c 1996 by Steve Hetzler and Bob Tardiff Department of Mathematics and Computer Science, Salisbury State University, Salisbury, MD 21801.