Comment by pfortuny

Tje difference is because we cannot easily tell between “curve of second order” and “curve of other order”.

You can get an idea when you try to understand why the function

y=0 for x<0 y=x^2 for x>=0

has two derivativea but not three.

But the issue is infinitesimal, so very hard to tell.

Jerk you can “linearise” if you think of a car (with no air friction) and its accelerator. Somehow…