>>12051097>>12051103based. By definition the best quadratic approximation of fitting a polynomial to the 'actual' polynomial is
The difference may feel subtle to a mathematician, but the experimentalist frequently grapples with this in the assumptions of their models. By what domain is their function smooth and bounded, so that inferences on the derivatives of a system, such as for physical systems, momentum.
It is of critical importance, in order to predict with accuracy, the trajectory of a particle, that one has knowledge of its higher order derivatives. resting here, tilting over a cliff, accelerating of a flat earth, jerking into the ether. I suppose this anon may be referring to the reality we don't use higher order derivatives than acceleration, like jerk or f''''' or f'''''''. I found this most evident through the theorems that make vector calculus valid like helmholtz, and of interesting consequence in electrodynamics. But anyways, I think at some point one has to question if the particle is moving, or on the strangest prestige of a ridiculously high moment (f''''''...) lol of a reaction. Again, maybe of little consequence to the meta-physicists, but for high precision measurement, engineering, high noise to signal ration, I think its worth grappling with this reality.
