py7.py

import matplotlib.pyplot as plt
import numpy as np

def f(x):
    return 2*x**2

# np.arrange(start, stop, step) to give us a smoother line
x = np.arange(0, 5, 0.001)
y = f(x)
plt.plot(x, y)

colors = ['k', 'g', 'r', 'b', 'c']

def approximate_tangent_line(x, approximate_derivative):
    return (approximate_derivative*x) + b

for i in range(5):
    # The point and the "close enough" point
    p2_delta = 0.0001
    x1 = i
    x2 = x1+p2_delta

    y1 = f(x1)
    y2 = f(x2)

    print((x1, y1), (x2, y2))

    # Derivative approximation and y-intercept for the tangent line
    approximate_derivative = (y2-y1)/(x2-x1)
    b = y2 - approximate_derivative*x2

    # plotting the tangent line
    # +/- 0.9 to draw the tangent line on our graph
    # then we calculate the y for given x using the tangent line function
    # Matplotlib will draw a line for us through these points
    to_plot = [x1-0.9, x1, x1+0.9]

    plt.scatter(x1, y1, c=colors[i])
    plt.plot([point for point in to_plot],
             [approximate_tangent_line(point, approximate_derivative) for point in to_plot], c=colors[i])

    print('Approximate derivative for f(x)', f'where x = {x1} is {approximate_derivative}')

plt.show()





plt.show()