import numpy as np

def newton_method(x0, N, f, df):
    x = x0;
    x_list = [x0];
    for i in range(N):
        x = x - f(x)/df(x);
        x_list.append(x)
    return x, x_list

N = 5;
x0 = 4
f = lambda x: (x-2)**3
df = lambda x: 3*(x-2)**2
x_true = 2

x, x_list = newton_method(x0, N, f, df);


for i in range(len(x_list)):
    rel_err = (x_list[i]-x_true)/x_true
    ei = abs(x_list[i]-x_true) 
    print("i: %2d, x: %15.13f rel err: %10e, e_{i} %10e" % (i, x_list[i], rel_err, ei));