import numpy as np 
import matplotlib.pyplot as plt
import math as math

def F(x):
    return x**2+3*x+1
x=np.linspace(-10,10)

h=0.1
x_Tan=np.linspace(-10,10)

for a in range(-10,10):
    d=(F(a+h)-F(a))/h
    Tangente= F(a)+d*(x_Tan-a)
    plt.plot(x_Tan, Tangente, color="#00BFBF")
    plt.plot(a, F(a), 'om')

plt.plot(x,F(x), color="Red", label=f'Función f(x)=χ²+3χ+1')
plt.axhline(0,color="Black")
plt.axvline(0,color="Black")

plt.xlabel('x')
plt.ylabel('y')
plt.title('Función f(x)=χ²+3χ+1')
plt.savefig("output.png")

plt.legend()
plt.show()

import numpy as np
import sympy as sym
import matplotlib.pyplot as plt
from tkinter import *

def calculate_polynomial():
    x = sym.Symbol('x')
    f = sym.exp(-2*x)
    x0 = 0
    grado = 6 
    n = grado + 1 
    k = 0
    polinomio = 0

    while (k < n):
        derivada = f.diff(x,k)
        derivadax0 = derivada.subs(x,x0)
        divisor = np.math.factorial(k)
        terminok = (derivadax0/divisor)*(x-x0)**k
        polinomio = polinomio + terminok
        k = k + 1
    print(polinomio)
    return polinomio

x = sym.symbols('x')
f = sym.exp(-2*x) 

plt.axhline(0, color="black")
plt.axvline(0, color="black")
polynomial = calculate_polynomial()
x_values = np.linspace(-10, 15, 50)
polynomial_fn = sym.lambdify(x, polynomial, 'numpy')
polynomial_values = polynomial_fn(x_values)
plt.plot(x_values, polynomial_values, color='blue', label=f'polinomio en grado n=6')
f_fn = sym.lambdify(x, f, 'numpy')
f_values = f_fn(x_values)
plt.plot(x_values, f_values, color='red',  label=f'e^(-2x)')
plt.xlim(-5,15)
plt.ylim(-5,20)
plt.xlabel('X')
plt.ylabel('Y')
plt.title('Polinomio de tylor para f(x)= e^(-2x)')
plt.legend()
plt.show()