¡¥he following properties: (a) Linearity property. If c1 and c2 are constants, then Tn(c1f + c2g) = c1Tn(f) + c2Tn(g) (b) Differentiation property. The derivative of a Taylor polynomial of f is a Taylor polynomial of f`; in fact, we have (Tnf)` = Tn-1(f`). / 7. Polynomial Approximations to Functions. Theorem 7.1. Let f be a function with derivatives of