Check a derivative by computer

You will write a numerical slope and use it to test a derivative formula, an implicit slope and a parametric slope. A computer cannot prove a formula, but it catches nearly every slip.

The idea. A slope taken on both sides of $x$, $\dfrac{f(x + h) - f(x - h)}{2h}$, is very close to $f'(x)$ for a tiny $h$. For a parametric curve, $\dfrac{dy}{dx}$ is the slope of $y$ divided by the slope of $x$, both taken against $t$.

Your tasks.

1. Finish slope(f, x). Return (f(x + H) - f(x - H)) / (2 * H).
2. Finish param_slope(xf, yf, t). Return the slope of yf at t divided by the slope of xf at t.
3. Finish matches(f, formula, points). Return True when formula(p) is within 0.001 of slope(f, p) for every p in points.