Newton avec iteration

def f(x):
    return (2*x**4+x**2+2)/(x**4+1)

def f_prime(x):
    return -4*x**3*(2*x**4 + x**2 + 2)/(x**4 + 1)**2 + (8*x**3 + 2*x)/(x**4 + 1)


def f_2prime(x):
    return 32*x**6*(2*x**4 + x**2 + 2)/(x**4 + 1)**3 - 8*x**3*(8*x**3 + 2*x)/(x**4 + 1)**2 -12*x**2*(2*x**4 + x**2 + 2)/(x**4 + 1)**2 + (24*x**2 + 2)/(x**4 + 1)
def newton_f_opt(x0, f_prime, f_2prime, maxiter = 100, tol = 0.0001):
    x = x0
    Nter = 0
    for i in range(maxiter):
        Nter += 1
        x_next = x - (f_prime(x)/f_2prime(x))
        if x_next - x < tol:
            return x_next, Nter+1
            print('Optimization terminated successfully.')
            print('Current parameter value: ' + str(x))
            print('Iterations: ' + str(i))
            break
        x = x_next

    if i == maxiter - 1 and x_next - x < tol:
        print('Optimization terminated after maximum number of iterations.')

    return x, Nter+1

x_star, Niter = newton_f_opt(0, f_prime, f_2prime)

print(x_star)
print(f(x_star))
print(Niter)