\subsection{Solution}


The best possible value of $m$ is the value that minimizes the
function $V_2(m)$. If we plot the function in Mathematica we get
\begin{center}
\includegraphics[width=0.75\textwidth]{Problem1/V2_graph.eps}
\end{center}
From the graph of function we can see that this is
the same as the value of $m$ at which $\dps\dif{V_2}{m}=0$. We can use
Mathematica to find the derivative of $V_2(m)$ by typing 
\verb+D[V2[m],m]+ The output is: 

\begin{center}
\includegraphics[width=\textwidth]{Problem1/V2_derivative.eps}
\end{center}
Then to solve  $\dps\dif{V_2}{m}=0$, we can type
\texttt{Solve[D[V2[m],m]==0,m]} and if this fails to work we can use \texttt{FindRoot[D[V2[m],m]==0,\{m,\{1.3,1.5\}\}]}.


