MATHEMATICS · Multi-part · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
A function h is analytic at x=1. Its third–degree Taylor polynomial about x=1 is
P3(x)=9+4(x−1)+k(x−1)2−4(x−1)3,
where k is a real constant.
(a) Given that h′′(1)=12, determine the value of k.
(b) Find h′′′(1).