Left and right derivatives by computer

You will write functions that estimate the left and right derivatives of a function at a point, and decide whether the function is differentiable there. The checker uses a smooth function, a corner and a join of two pieces.

The idea. The left derivative is the slope of the chord from a point just left of $a$ to $a$. The right derivative is the slope of the chord from $a$ to a point just right of $a$. A function is differentiable at $a$ when the two agree.

Your tasks.

1. Finish left_derivative(f, a). Return (f(a) - f(a - H)) / H.
2. Finish right_derivative(f, a). Return (f(a + H) - f(a)) / H.
3. Finish is_differentiable(f, a). Return True when the two derivatives differ by less than 0.001.