) = a_0$ </td><td> $a_0=36\pi$ </td></tr>
<tr><td> $1$ </td><td> $V'(3) = 4\pi (3)^2=36\pi$ </td><td> $P'(3) = a_1$ </td><td> $a_1=36\pi$ </td></tr>
<tr><td> $2$ </td><td> $V''(3) = 8\pi (3)=24\pi$ </td><td> $P''(3) = 2a_2$ </td><td> $2a_2=24\pi$ </td></tr>
<tr><td> $3$ </td><td> $V'''(3) = 8\pi$ </td><td> $P'''(3) = 6a_3$ </td><td> $6a_3=8\pi$ </td></tr>
        </table>  

<p>This tells us that the third order polynomial is
    $$P(r)=a_0+a_1(r-3)+a_2(r-3)^2+a_3(r-3)^3
    =36\pi+36\pi(r-3)+12\pi(r-3)^2+\