Count the corners

You will write a program that finds the corners of a function from the slopes on its two sides. It checks a list of candidate points and reports the ones where the slopes differ. The checker uses absolute values, a double zero and a product.

The idea. At a candidate point $a$, the left slope is $\dfrac{f(a) - f(a - h)}{h}$ and the right slope is $\dfrac{f(a + h) - f(a)}{h}$ for a tiny $h$. If they differ by more than $0.001$, the point is a corner.

Your tasks.

1. Finish slopes(f, a). Return the pair (left, right), with H = 0.000001.
2. Finish is_corner(f, a). Return True when the two slopes differ by more than 0.001.
3. Finish corners(f, candidates). Return the list of candidates at which f has a corner.