The table lists the values of the first three derivatives of an unknown function at
MATHEMATICS · Multi-part · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
The table lists the values of the first three derivatives of an unknown function h at x=2.
k
h(k)(2)
0
1.500
1
-0.750
2
4.200
3
-6.600
Assume h is sufficiently differentiable for the work below.
(a) Using only the data in the table, write the third-degree Taylor polynomial Q3(x) for h centered at x=2.
(b) Use Q3 to estimate h(1.8). Show numerical substitution clearly.
(c) Interpret the coefficient of the (x−2)2 term in Q3 in terms of the behavior of h near x=2.