Animate movement of Tangent line across graph

Question

Background

Hello - I'm a new math's teacher and I've thought on how to illustrate the concept of derivatives. I would like to make a gif or a video (don't really care which one) of a tangent line moving along a graph.

I've tried many different ways, and most of the videos/ posts I've read, shows a graph being constructed as x changes... This is not really what I'm looking for, as following those videos I can also construct my graph. But I want a straight line changing its slope at each point along the graph.

# Define parabola
def f(x):
    return 5*x**3-2*x**2-2*x

# Define parabola derivative
def slope(x):
    return 15*x**2-4*x-2

# Define tangent line
def line(x, x1, y1):
    return slope(x1)*(x - x1) + y1

My question

are there any good examples of how this might be done? maybe videos or codes I could look at for inspiration?

I know my question is a bit vague, but thanks in advance

Answer 1

You could use the FuncAnimation function that matplotlib provides (see doc here).

Below is an example with the code you provided:

import matplotlib.pyplot as plt
import numpy as np
from matplotlib.animation import FuncAnimation

# Define parabola
def f(x):
    return 5*x**3-2*x**2-2*x

# Define parabola derivative
def slope(x):
    return 15*x**2-4*x-2

# Define tangent line
def line(x, x1, y1):
    return slope(x1)*(x - x1) + y1


###Set up animation###
fig, ax = plt.subplots()
range_x=np.linspace(-1,1,100,endpoint=True)
range_slope=np.linspace(-1,1,100,endpoint=True)
plt.plot(range_x, f(range_x),'ro',label='Parabola')
ln_slope,=plt.plot([],[],'tab:blue',label='Tangent',lw=3.5)
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.legend(loc='upper right')


def init():
    ax.set_xlim(-1,1)
    ax.set_ylim(-6, 3)
    
    return ln_slope,


def update(frame):
    ydata=line(range_slope,range_x[frame],f(range_x[frame]))

    ln_slope.set_data(range_slope, ydata)
    return ln_slope,

ani = FuncAnimation(fig, update, frames=100,init_func=init, blit=True)
plt.show()

And the output gives: