A function has a Taylor polynomial centered at given by P(x)=1+4(x-2)+ 3 2 (x-2)^2+ 1…

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

Problem

A function

p

has a Taylor polynomial centered at

x=2

given by

P(x)=1+4(x-2)+\frac{3}{2}(x-2)^2+\frac{1}{6}(x-2)^3.

What are

p'(2)

and

p''(2)

? (a)

p'(2)=2\text{ and }p''(2)=3

(b)

p'(2)=4\text{ and }p''(2)=\dfrac{3}{2}

(c)

p'(2)=4\text{ and }p''(2)=3

(d)

p'(2)=3\text{ and }p''(2)=4