From: utzoo!decvax!harpo!npoiv!alice!rabbit!ark
Newsgroups: net.misc
Title: Re: Using Taylor Series To Extrapolate
Article-I.D.: rabbit.649
Posted: Sat Jul 31 22:29:26 1982
Received: Sun Aug  1 03:25:32 1982
References: eagle.435

It is indeed true that you can extrapolate the behavior of
a function everywhere from its behavior at a single point,
provided that (a) "behavior" means "value of the function
and all its derivatives," and (b) the function and all its
derivatives are continuous (and, by implication, differentiable)
everywhere.