Answer:
Explanation:
Sure, I can help you with that! Here's an example Python code for creating a cobweb graph showing Newton's method:
import numpy as np
import matplotlib.pyplot as plt
# Define the function and its derivative
def f(x):
return x**3 - x**2 - x - 1
def df(x):
return 3*x**2 - 2*x - 1
# Define the Newton's method
def newton(x0, f, df, n):
x = [x0]
y = [f(x0)]
for i in range(n):
x.append(x[-1] - f(x[-1])/df(x[-1]))
y.append(f(x[-1]))
return x, y
# Set the initial values
x0 = 1.5
n = 15
# Calculate the points for the cobweb graph
x, y = newton(x0, f, df, n)
xs = np.linspace(min(x+y), max(x+y), 1000)
ys = f(xs)
# Plot the cobweb graph
plt.plot(xs, ys, 'b-', label='f(x)')
plt.plot(xs, xs, 'k--', label='y=x')
plt.plot(x, y, 'ro-', label='Newton\'s method')
plt.xlabel('x')
plt.ylabel('f(x)')
plt.legend()
plt.title('Cobweb graph for Newton\'s method')
plt.show()
In this code, the f(x) and df(x) functions represent the function and its derivative, respectively, while the newton() function implements Newton's method to calculate the roots of the function. The x0 variable represents the initial guess, and the n variable controls the number of iterations to perform.
The xs and ys variables are used to calculate the points for the cobweb graph, which are then plotted using Matplotlib. The plot() function is used to plot the function f(x) in blue, the line y=x in black, and the points generated by Newton's method in red.
You can modify this code to use your own function and initial values, and adjust the parameters to produce different cobweb graphs.