Check an antiderivative by computer

You will write three small functions. The first estimates the slope of a function at a point. The second tests whether a function is an antiderivative of another. The third finds the constant of integration from a point on the curve.

The idea. If $F$ is an antiderivative of $f$, the slope of $F$ at every point equals $f$ there. The slope at $x$ is estimated from two nearby points: $\dfrac{F(x + h) - F(x - h)}{2h}$ for a tiny number $h$.

Your tasks.

1. Finish slope(F, x). Return the estimate above, with h = H.
2. Finish is_antiderivative(F, f, points). Return True when the slope of F is within 0.0001 of f at every point in the list.
3. Finish constant_for(F, x0, y0). Return the number C so that F(x) + C passes through the point (x0, y0).