from sympy import symbols, expand, prod import numpy as np

Given data points

x_values = [1, 3, 5, 6] y_values = [18, -8, 30, 88]

Define the variable

x = symbols('x')

Function to calculate the Lagrange polynomial

def lagrange_interpolation(x_values, y_values, x): n = len(x_values) lagrange_poly = 0 for i in range(n): # Calculate each Lagrange basis polynomial basis_poly = prod([(x - x_values[j]) / (x_values[i] - x_values[j]) for j in range(n) if i != j]) lagrange_poly += y_values[i] * basis_poly return expand(lagrange_poly)

Calculate the Lagrange polynomial

lagrange_poly = lagrange_interpolation(x_values, y_values, x)

Find f(12)

f_12 = lagrange_poly.subs(x, 12)

lagrange_poly, f_12(x3 - x2 - 22x + 40, 1360)(x3 - x2 - 22x + 40, 1360)successThe