(adsbygoogle = window.adsbygoogle || []).push({}); 1. Construct a function f (x) so that Newton's method gets 'hanging' in an infinite cycle x_{n}= (-1)^{n}x0 , no matter how the

start value x_{0}is chosen.

2. Relevant Equations:

x_{n+1}= x_{n}- f(x_{n}) / f'(x_{n})

3. The attempt at a solution

x_{n+1}= x_{n}- f(x_{n}) / f'(x_{n}) = (-1)^{n+1}x_{0}= (-1)^{n}x_{0}- f(x_{n}) / f'(x_{n}) [itex]\Rightarrow[/itex] f(x_{n}) / f'(x_{n}) = 2(-1)^{n}x_{0}

But, I don't know if that's what I wanna do or what to do with it.

Any ideas?

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# Newton's Method for Root Finding - Infinite Loop

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