Newton's Method Help [0/1]

*To*: mathgroup at smc.vnet.net*Subject*: [mg5072] Newton's Method Help [0/1]*From*: rligeski at webbernet.net*Date*: Fri, 25 Oct 1996 22:48:17 -0400*Organization*: WebNet*Sender*: owner-wri-mathgroup at wolfram.com

Hello, In my calculus class we just began using Mathematica for Newtons method. We were given a lab to do involving the method, but there is a special program so we can use Newton[] and NewtonTable[]. The former takes the equation with an initial guess goes through a certain number of iterations and then graphs each of them. The latter does the same thing except it puts it into a table format instead of graphing. I do understand Newtons method. We were given 2 problems that no one in my class can get. He won't help us because he thinks we should be able to do it. I was wondering if someone could help me with the problems. They are: 1. Find a polynomial F so that Newton's method fails to converge in the following way for X(sub 0)=1. The first iteration gives X(sub 1)= -1, the next X(sub 2)= -2, and X(sub 3)=X(sub 0] the starting point. Assume F(1)=1, F(-1)=2, and F(-2)=3 2. Find a polynomial F which fails as above but which also has one root between -1 and 1 at 0; that is in addition to values given above, F(0)=0 The teacher did give us a hint, he said sketch it first. I did this but don't know how to use Mathematica well enough to do this. I also searched the Mathematica website but that did not help. I am going to include the notebook that we used in school, because this is not standard. I would appreciate it if someone would try to help me. Thank You, Brian Ligeski