The derivative from the definition

You will write three functions that find a derivative by computer, using the definition with a very small $h$. The checker uses $x^2$ and $x^3 - 3x$.

The idea. The slope of the secant through $(a, f(a))$ and $(a + h, f(a + h))$ is $\dfrac{f(a + h) - f(a)}{h}$. For a very small $h$ it is almost the derivative. The tangent at $a$ is $y = mx + c$ with $m = f'(a)$ and $c = f(a) - m\,a$.

Your tasks.

1. Finish secant_slope(f, a, h). Return the slope of the secant through $x = a$ and $x = a + h$.
2. Finish derivative_at(f, a). Use secant_slope with h = 0.000001.
3. Finish tangent_line(f, a). Return the pair (m, c) of the tangent line y = m * x + c.