import numpy as np

x_k = 2  # Initial (guessed) value
K = 0.01  # Parameter
prec = 0.0001 #  Precision of result
max_iter = 10000  #  Max number of iterations
k = 0
df_min = np.inf

def f(x):
    return x**2 + 1

# Derivative
def df(x):
    return 2*x

while (k < max_iter) and (abs(df_min) > prec):
    
    x_kp1 = x_k - K*df(x_k)  # kp1 means 'k plus 1'.
    df_min = df(x_k)
    x_k = x_kp1
    k += 1

print('y_min = ', f(x_k))
print('x_opt = ', x_k)
print('k = ', k)
print('df =', df_min)