Taylor Polynomials Approximated by Interpolations

distribution of points

number of points

2

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

n

(gold) for the curve

y=f(x)

at

x=1

can be approximated by interpolating

n

points on the curve around

x=1

(blue). The proof is not simple, but straightfoward using divided differences.