In the neighbourhood of , for the best possible choice is always , and for the best possible choice is always . For , , and higher-degree coefficients, these coefficients are determined by higher derivatives of . should always be , and should always be . Using these coefficients gives the Taylor polynomial of . The Taylor polynomial of degree is the polynomial of degree which best approximates , and its coefficients can be found by a generalization of the above formulas. Taylor's theorem gives a precise bound on how good the approximation is. If is a polynomial of degree less than or equal to , then the Taylor polynomial of degree equals .