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## Homework Statement

Use newtons method to compute the cube root of 5. Do the first 10 iterations. [itex]x_{(0)}=1[/itex]

determine the fixed points of the iteration and determine whether they are repelling/attracting. if attracting, then determine if the convergence is linear or quadratic. draw the x[itex]^{(k+1)} vs. x^{(k)}[/itex] diagram. for what values of [itex]x^{(0)}[/itex] does newton's method converge?

## The Attempt at a Solution

So i did the first 10 iterations for x^(n). After n=5, all following iterations will give the same value.

I am confused as to how we determine what the fixed points are and whether they are attracting/repelling.