# Taylor Polynomials Approximated by Interpolations

Taylor Polynomials Approximated by Interpolations

Taylor polynomials are usually introduced as an extension of the analytic definition of a tangent line, but they can be approximated by interpolations as well. The program illustrates that the Taylor polynomial of degree (gold) for the curve at can be approximated by interpolating points on the curve around (blue). The proof is not simple, but straightfoward using divided differences.

n

y=f(x)

x=1

n

x=1