How to plot the slope (tangent line) of parabola at any point?

Question

I want to plot a simple illustration of using derivative to find out a slope of a function at any point. It would look kinda like this:

I have already plotted a simple parabola using this code:

import numpy as np
from matplotlib import pyplot as plt

inputs = 0.2
weights = np.arange(-6,14)
target_prediction = 0.7

prediction = inputs*weights
errors = (prediction - target_prediction) ** 2
plt.xlabel("Weight")
plt.ylabel("Error")
plt.plot(weights, error)

Now I want to add something like this:

current_weight = 5
# draw a short fraction of a line to represent slope
x = np.arange(optimal_weight - 3, optimal_weight + 3)
# derivative
slope = 2 * (inputs*current_weight - target_prediction)
y = slope*x # How should this equation look like?
plt.plot(x, y)

To draw a tangent line going through the current_weight.

But I can't seem to figure this out, can you help?

Answer 1

Once you have the slope at the desired point, you need to write the equation for the tangent line using point-slope form:

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

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

# Define x data range for parabola
x = np.linspace(-5,5,100)

# Choose point to plot tangent line
x1 = -3
y1 = f(x1)

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

# Define x data range for tangent line
xrange = np.linspace(x1-1, x1+1, 10)

# Plot the figure
plt.figure()
plt.plot(x, f(x))
plt.scatter(x1, y1, color='C1', s=50)
plt.plot(xrange, line(xrange, x1, y1), 'C1--', linewidth = 2)

You can do this for any differentiable function, and can use derivative approximation methods (such as finite differencing) to eliminate the need to provide the analytical derivative.