import numpy as np

# %% Function f(x):

def fun_f(x):
    f = (x + 1)*(x - 1)   
    return f

# %% Function df_dx:

def fun_der_f(x):
    der_f = 2*x   
    return der_f

# %% Initialization:

x_n = 2
f_tol = 0.001
n = 0
f_abs_n = np.inf
n_max = 50

# %% Iterations with while loop:

while (abs(fun_f(x_n)) > f_tol and (n < n_max)):
    x_np1 = x_n - fun_f(x_n)/fun_der_f(x_n) # Newton step
    x_s = x_np1  # Candidate of solution
    x_n = x_np1  # Index shift (preparing for next iter.)
    n += 1  # Updates number of iterations
        
# %% Displaying results:

print('x_s = ', x_s)
print('n = ', n)