"""
Example from lecture 17/10. A class for representing
the derivative of a function. This is useful for instance
in Newton's method, which requires both the function f in
f(x) = 0 and its derivative.
"""




class Derivative:
    def __init__(self, f, h=1E-5):
        self.f = f
        self.h = float(h)

    def __call__(self, x):
        f, h = self.f, self.h      # make short forms
        return (f(x+h) - f(x))/h



def f(x):
    return 4 * x**2 + 8 * x


df = Derivative(f)
print('f = 4 * x**2 + 8x, x= 2:')
print(f'True derivative: {8 * 2 + 8:.3f}')
print(f'"Automatic" derivative: {df(2):.3f}')

"""
Terminal> python derivative.py 
f = 4 * x**2 + 8x, x= 2:
True derivative: 24.000
"Automatic" derivative: 24.000
"""