import numpy as np
from matplotlib import mlab
import matplotlib.pyplot as plt



def f(x):
    return 6*x**5-5*x**4-4*x**3+3*x**2

def df(x):
    return 30*x**4-20*x**3-12*x**2+6*x

def dx(f, x):
    return abs(0 - f(x))

def tangent(x):
    return -0.0625 - 1.625 * x

def newtons_method(f, df, x0, e):
    delta = dx(f, x0)
    while delta > e:
        x0 = x0 - f(x0)/df(x0)
        delta = dx(f, x0)
    print('root: ', x0)
    print('f(x) = ', f(x0))


def plot(point):
    xmin = -1.0
    xmax = 1.5

    dx = 0.01

    xlist = mlab.frange(xmin, xmax, dx)

    ylist1 = [f(x) for x in xlist]
    ylist2 = [tangent(x) for x in xlist]

    plt.figure("Newtone's method")
    plt.plot(xlist, ylist1)

    scatter1 = plt.scatter(0.0, 0.0)
    scatter2 = plt.scatter(point, 0.0)

    plt.errorbar(point, 0, xerr=0.08, yerr=1)
    plt.plot(xlist, ylist2)

    plt.tight_layout()
    plt.grid()
    plt.show()


def main():
    x0s = float(input('>> '))
    newtons_method(f, df, x0s, 1e-5)
    plot(x0s)

if __name__ == '__main__':
    main()