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Up: Newton's Method
- Use the Newton command with the function f from the
examples and the starting value x=1.1.
- Describe what happens when Newton's method is used with this
initial condition. You might want to use NewtonPlot to help
you understand what is going on. Start with just a few iterations, and
then increase the number of iterations slowly. The maximum number of
iterations you use should not exceed fifty.
- What value of n is required to guarantee that for all ?
- Use the Newton command to find an approximation to the
root near x=-2 of the equation
- Consider the function g from the examples.
- Can you explain, using the graph of g and perhaps the
NewtonPlot command, why Newton's method fails to converge for
the initial guess x=0?
- Find approximations to all of the roots of g. How do you know
that you have found all of the roots?
William W. Farr