Attractiver vs super attractive Newton's method

mark
Tue, 19 Sep 2017 13:28:37 +0000
Quiz or Test Prep

Let [imath]k[/imath] be an integer and let [imath]f(x)=k x + x^2[/imath].

Find the Newton's method iteration function [imath]N[/imath] for [imath]f[/imath] and simplify it.

Show that the origin is super attractive if [imath]k\neq 0[/imath] but that it is just attractive if [imath]k=0[/imath].