A function satisfies for all

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

A function satisfies

f^{(3)}(x)=12

for all

x

, with initial conditions

f''(0)=3

f'(0)=-2

, and

f(0)=1

. Which expression for

f(x)

is consistent with all of the given information? (a)

2x^{3}+3x^{2}-2x+1

(b)

2x^{3}+\dfrac{3}{2}x^{2}-2x

(c)

2x^{3}+\dfrac{3}{2}x^{2}-2x+1

(d)

4x^{3}+\dfrac{3}{2}x^{2}-2x+1