def f(x):
    return 4*x - 1.8*x*x + 1.2*x*x*x + - 0.3*x*x*x*x


def f_prime(x):
    return -1.2*x*x*x + 3.6*x*x - 3.6*x + 4


def f_prime_prime(x):
    return -3.6*x*x + 7.2*x - 3.6


def newton(x0, max_error, iterations):
    x = x0
    error = 1
    ite = 0
    while error > max_error and ite < iterations:
        temp = x
        x = x - f_prime(x) / f_prime_prime(x)
        ite += 1
        error = abs(x - temp) / x
    return [x, f(x), error, ite]


res = newton(0, 1e-2, 100)

print('The maximum of function f(x) is', res[1], 'at x =', res[0])
exit()