[math]f[/math] is a function which has derivatives of all orders at a point [math]A=(a, f(a))[/math] on a graph of [math]f[/math].[br]We have a following Taylor series[br][br][math]f(x)=\sum_{n=0}^{\infty}\frac{f^{(n)}(a)}{n!} (x-a)^2[/math][br][br]Any finite number of initial terms of the Taylor series of a function is called a Taylor polynomial.[br]Taylor polynomials can be used as approximations of the function.