Explanation of Newton's Method

[oreon]

Hi everybody, I have a kinda theory to explain but I need a little help to find out the explanation of it. It is,

suppose your first guess using Newton's method to find a root is lucky and you guess the exact root of f(x). (Not an approximation,but exact) What happens to your second approximation of the root and later approximations? Justfiy the answer with calculus and specific examples.

do I fail when I do the second approximation of the root and for the other approximations? and how does that happen?

I got liitle bit confuse about this.

[Muzza]

Just look at the formula used in Newton's method:

x_(n + 1) = x_n - f(x_n) / f'(x_n).

What happens if f(x_n) = 0? How can x_(n + 1) be simplified then?

[oreon]

so you are saying that, if it is equal to zero, then it can not be simplified.

Am I right sir?

[arildno]

What it says is then that x(n+1)=x(n)

[oreon]

Oh I got it. Thank you for your helps...