Mathematics

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}

\displaystyle \tfrac{23}{3}

\displaystyle \tfrac{31}{3}

\displaystyle \tfrac{11}{3}