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

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.