Newton's Method w/ cot

[dear2009]

Hello everyone,


Apply Newton's method to find a root of

f(x) = x^3 - cot(pi)(x)

in the interval (0, 1). If your initial guess is x0 = 1/2 then x1 = ?


This is what I did so far
F(x) = x - [f(x) - f'(x)
= x - (x^3 - cot(pi)(x)/ (3x^2 - (pi)(?)(cotangent)(pi)

I am lost after this step, so any help would be greatly appreciated.

 

[Deleted member 4993]

Hello everyone,


Apply Newton's method to find a root of

f(x) = x^3 - cot[(pi)(x)]

in the interval (0, 1). If your initial guess is x0 = 1/2 then x1 = ?


This is what I did so far
F(x) = x - [f(x) - f'(x)
= x - (x^3 - cot(pi)(x)/ (3x^2 - (pi)(?)(cotangent)(pi) <<< These steps are irrelevant to Newton_Raphson's method of finding roots of a polynomialI am lost after this step, so any help would be greatly appreciated.

1) find f'(x)

2)estimate root from graph or other suitaable metod (x[sub:11n1wzxa]o[/sub:11n1wzxa]).

3) choose iteration stopping criterion ? such that |f(x[sub:11n1wzxa]o[/sub:11n1wzxa])|? ? - you are going to call it close enough

4) Evaluate f(x[sub:11n1wzxa]o[/sub:11n1wzxa]) - and check step (3)

5) Evaluate f'(x[sub:11n1wzxa]o[/sub:11n1wzxa]) and f(x[sub:11n1wzxa]o[/sub:11n1wzxa])/f'(x[sub:11n1wzxa]o[/sub:11n1wzxa])

6) new estimate of root x[sub:11n1wzxa]n[/sub:11n1wzxa]= x[sub:11n1wzxa]o[/sub:11n1wzxa] - f(x[sub:11n1wzxa]o[/sub:11n1wzxa])/f'(x[sub:11n1wzxa]o[/sub:11n1wzxa]) and x[sub:11n1wzxa]o[/sub:11n1wzxa] = x[sub:11n1wzxa]n[/sub:11n1wzxa]

7) go to step (4)

 

[dear2009]

Dear Subhotosh Khan,


Do you mind showing me the steps from 1 and 2, I believe I can get to step 3 if i know how to start with these two steps. Thanks in advance.

 

[Deleted member 4993]

The first step is to differentiate the given function. If you are trying to learn Newton's method - you surely know how to differentiate.