Find and classify the critical points

You will write three functions that work with any smooth function $f$ given as a Python function: the derivative at a point, the critical points on an interval, and the kind of a critical point. The checker tests several functions.

The idea. The derivative can be found from a very short balanced interval. A critical point lies where $f'$ changes sign, so we scan a fine grid and look for a change of sign between neighbouring points. The first derivative test then looks at the sign of $f'$ just before and just after the point.

Your tasks.

1. Finish slope(f, x). Use the interval from x - h to x + h, with h = 1e-6.
2. Finish critical_points(f, a, b). The list xs holds a fine grid of points on $[a, b]$. Return the point half way between two neighbouring grid points where slope changes sign, rounded to 2 decimal places.
3. Finish classify(f, c). Return "maximum", "minimum" or "neither" from the signs of slope at c - 0.01 and c + 0.01.