[palish]

But those tend not to have a zero derivative at the vertices, no? Which would cause other animation problems, if you try to link two curves together.

[saucerful]

Yes, a quadratic Bezier is only piecewise differentiable. If you need it to be completely smooth you can use a higher order Bezier (i.e. a higher order polynomial).

But the reality is that if the curve looks pretty smooth, the animation will be pretty smooth. By computing the change in derivative at the singular point you can figure out how big the jump is, and then try to minimize it.