[toolslive]

well, from memory (this was > 20y ago)

  - Taylor gives you polynomial optimized for the evaluation of one point.
  - naive Newton gives you a polynomial with 0 error in the interpolation points [but the system has a bad condition]
  - Chebychev gives you a polynomial with minimal error over the interval of choice.

So there is no real reason to ever use the Taylor series to approximate a function over an interval. The high school math teachers are lying.

[rmorey]

not lying, probably just mistaken