The Maclaurin polynomial of a function is P_4(x)=5+4x+bx^ 2 + c 6 x^ 3 + d 24 x^ 4

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

Problem

The Maclaurin polynomial of a function

f

P_4(x)=5+4x+bx^{2}+\frac{c}{6}x^{3}+\frac{d}{24}x^{4}.

The derivatives of

f

x=0

satisfy

f''(0)=f'(0)+2

and

f'''(0)=3f''(0)-6

. What is the value of

c

? (a)

6

(b)

24

(c)

12

(d)

18