Example 3

In the first two frames, we see the standard process moving from x₀ to x₁. Notice that in this example, each estimate is less than the previous estimate. In fact, since all tangent lines have positive slope for this graph, each estimate will be less than the previous estimate no matter how long we iterate Newton's Method. Even worse, the difference between each estimate and the next is increasing! The estimates are not settling down near any particular value; they are moving away from each other at an ever increasing rate. The problem for Newton's Method in this example is that there is no solution. The graph never crosses the x-axis.

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