Test a solution by computer

You will write three small functions. The first estimates $y'$ from two nearby points. The second estimates $y''$ from three nearby points. The third tests whether a function is a solution of $y'' - 3y' + 2y = 0$.

The idea. A solution makes $y'' - 3y' + 2y$ equal to zero at every point. We cannot test every point, so we test a few. The estimates are $y' \approx \dfrac{y(x + h) - y(x - h)}{2h}$ and $y'' \approx \dfrac{y(x + h) - 2y(x) + y(x - h)}{h^2}$ for a tiny number $h$.

Your tasks.

1. Finish first(f, x). Return the estimate of $y'$ above, with h = H.
2. Finish second(f, x). Return the estimate of $y''$ above.
3. Finish is_solution(f, points). Return True when $y'' - 3y' + 2y$ is within 0.001 of zero at every point of the list.