In [4]: 
import numpy as np
import matplotlib.pyplot as pt

Task: Approximate a function (here: by a line)

In [5]: 
def f(x):
    return - x**2 + 3*x

def df(x):
    return -2*x + 3

center = -1
dist = 3
grid = np.linspace(center-dist, center+dist, 100)

fx = f(grid)
pt.plot(grid, fx)
pt.plot(grid, f(center) + df(center) * (grid-center))

pt.xlim([grid[0], grid[-1]])
pt.ylim([np.min(fx), np.max(fx)])
Out[5]:
(-28.0, 2.2497704315886136)