A twice–differentiable function satisfies for all real

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

Problem

A twice–differentiable function

h

satisfies

h''(t)=3t^{2}-2t+1

for all real

t

. In addition,

h'(0)=4

and

h(0)=-1

. What is the value of

h(2)

? (a)

\displaystyle \tfrac{25}{3}

(b)

\displaystyle \tfrac{23}{3}

(c)

\displaystyle \tfrac{31}{3}

(d)

\displaystyle \tfrac{11}{3}

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