newton

import matplotlib.pyplot as plt
import numpy as np

def f(x):
    return np.log(x)
x0, x, x1, x2  = 1, 2, 4, 6

A0 = f(x0)
A1 = ((f(x1) - f(x0)) / (x1 - x0))
A2 = (((f(x2) - f(x1)) / (x2 - x1)) - A1) / (x2 - x0)

result = A0 + A1 * (x - x0) + A2 * ((x - x0) * (x - x1))

print(result)

val_x = np.linspace(.01, 5, num = 100)
plt.plot(val_x, f(val_x), 'b')
plt.plot(2, result, 'ro')
plt.plot(2, f(2), 'go')
plt.show()