Graphing Tangent Lines with Python

By: Tao Steven Zheng

Import these libraries

import matplotlib.pyplot as plt
import numpy as np

Part 1: Calculating Derivatives on Python

def deriv(f,x):

    h = 0.000000001                 #step-size 
    return (f(x+h) - f(x))/h        #definition of derivative

Part 2: Plot function with tangent

 def tangent_line(f,x_0,a,b):
    x = np.linspace(a,b,200)
    y = f(x) 
    y_0 = f(x_0)
    y_tan = deriv(f,x_0) * (x - x_0) + y_0 
   
  #plotting
    plt.plot(x,y,'r-')
    plt.plot(x,y_tan,'b-')
    plt.axis([a,b,a,b])
    plt.xlabel('x')     
    plt.ylabel('y')    
    plt.title('Plot of a function with tangent line') 
    plt.show()    

Part 3: Tests and results

#Test number 1

def f1(x):
    return x**2

tangent_line(f1,1,-2,2)

#Test number 2

def f2(x):
    return np.exp(-x**2)

tangent_line(f2,1,-2,2)