Question

Suppose

t4(x) = 2 − 7(x − 3) + 3(x − 3)2


− 8(x − 3)3 + 3(x − 3)4


is the degree 4 taylor polynomial centered at


x = 3 for some function f.


what is the value of f


(3)(3)

Answer 1

f(3) = t4(3) = 2

The value of the function at the point of expansion is the first (constant) term of the Taylor series.