Let be a function whose derivatives at satisfy ,

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

Problem

Let

h

be a function whose derivatives at

x=2

satisfy

h(2)=4

h'(2)=-1

, and

h''(2)=6

. A cubic polynomial centered at

x=2

is constructed in the form

P(x)=4-\bigl(x-2\bigr)+3\bigl(x-2\bigr)^{2}+c\bigl(x-2\bigr)^{3}.

If one additionally requires that

P(3)=10

, what is the value of the coefficient

c

? (a)

2

(b)

4

(c)

-4

(d)

6