I mean, any smooth curve (without singularities) is well approximated by simple polynomials locally, which is simply its power series expansion. Doesn’t mean si

I mean, any smooth curve (without singularities) is well approximated by simple polynomials locally, which is simply its power series expansion. Doesn’t mean simple polynomials would necessarily hold much predicative power, however well they fit the current data. Higher order terms, if any, will come to dominate.