Suppose that an unspecified function f(:E) has the degree 7 Taylor polynomial at :1: = 0 : p7(:t:) = 2:1:7 19cc6 112:5 43:4. Because 7 p703) = 19230 fa\") (0)% you can read off the value of the derivatives of f(a:) at a: = 0 by looking at the coefficients of k 52! as follows: 331 - the coefficient of ? in p7(a:) is f(1)(0) = 0 0 2 . the coeffICIent of i In p7(a:) Is fa) (0) = 0 0 3 - the coeffICIent of y In 197(3) Is f(3) (0) = 0 0 it . the coeffICIent of F In 197(3) Is f(4) (0) = -. And so without differentiating, we see that the smallest positive integer n > 1 for which NWO) 0 is Hence the function has a local maximum 9 at a: = 0