tangent.py

%matplotlib inline
import matplotlib.pyplot as plt

# calculate the cost at -5
def f(w1):
    return np.mean((w1*data['speed'] - data['dist'])**2)

w1 = -5
h = 0.1
x_tan = np.linspace(-10, 0, 15)
gradient = (f(w1+h)-f(w1))/h # derivative
tan = f(w1)+gradient*(x_tan-w1)  # tangent

# plot the costs
plt.plot(range(-10,11,1), costs)
plt.plot(x_tan, tan, color='red')
plt.plot([-5], [f(-5)], marker='o', color='red')
plt.xlabel('w1')
plt.ylabel('cost')
plt.show()