The table gives values of the derivatives of a differentiable function at : f(2)=3

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

The table gives values of the derivatives of a differentiable function

f

x=2

f(2)=3,\quad f'(2)=-1,\quad f''(2)=4,\quad f^{(3)}(2)=0,\quad f^{(4)}(2)=-8.

Using the fourth-degree Taylor polynomial for

f

centred at

x=2

, which of the following is the best approximation of

f(1.9)

? (a)

3.118

(b)

3.120

(c)

3.100

(d)

3.140