Let $f , g : [ - 1,2 ] \rightarrow \mathbb { R }$ be continuous functions which are twice differentiable on the interval $( - 1,2 )$. Let the values of $f$ and $g$ at the points $- 1,0$ and 2 be as given in the following table:

\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
 & $x = - 1$ & $x = 0$ & $x = 2$ \\
\hline
$f ( x )$ & 3 & 6 & 0 \\
\hline
$g ( x )$ & 0 & 1 & - 1 \\
\hline
\end{tabular}
\end{center}

In each of the intervals $( - 1,0 )$ and $( 0,2 )$ the function $( f - 3 g ) ^ { \prime \prime }$ never vanishes. Then the correct statement(s) is(are)\\
(A) $\quad f ^ { \prime } ( x ) - 3 g ^ { \prime } ( x ) = 0$ has exactly three solutions in $( - 1,0 ) \cup ( 0,2 )$\\
(B) $f ^ { \prime } ( x ) - 3 g ^ { \prime } ( x ) = 0$ has exactly one solution in $( - 1,0 )$\\
(C) $f ^ { \prime } ( x ) - 3 g ^ { \prime } ( x ) = 0$ has exactly one solution in $( 0,2 )$\\
(D) $f ^ { \prime } ( x ) - 3 g ^ { \prime } ( x ) = 0$ has exactly two solutions in ( $- 1,0$ ) and exactly two solutions in ( 0,2 )