If $f ^ { \prime } ( x ) > 0$ for all real numbers $x$ and $\int _ { 4 } ^ { 7 } f ( t ) d t = 0$, which of the following could be a table of values for the function $f$ ? (A)
$x$
$f ( x )$
4
- 4
5
- 3
7
0
(B)
$x$
$f ( x )$
4
- 4
5
- 2
7
5
(C)
$x$
$f ( x )$
4
- 4
5
6
7
3
(D)
$x$
$f ( x )$
4
0
5
0
7
0
(E)
$x$
$f ( x )$
4
0
5
4
7
6
If $f ^ { \prime } ( x ) > 0$ for all real numbers $x$ and $\int _ { 4 } ^ { 7 } f ( t ) d t = 0$, which of the following could be a table of values for the function $f$ ?
(A)
\begin{center}
\begin{tabular}{ | c | c | }
\hline
$x$ & $f ( x )$ \\
\hline
4 & - 4 \\
\hline
5 & - 3 \\
\hline
7 & 0 \\
\hline
\end{tabular}
\end{center}
(B)
\begin{center}
\begin{tabular}{ | c | c | }
\hline
$x$ & $f ( x )$ \\
\hline
4 & - 4 \\
\hline
5 & - 2 \\
\hline
7 & 5 \\
\hline
\end{tabular}
\end{center}
(C)
\begin{center}
\begin{tabular}{ | c | c | }
\hline
$x$ & $f ( x )$ \\
\hline
4 & - 4 \\
\hline
5 & 6 \\
\hline
7 & 3 \\
\hline
\end{tabular}
\end{center}
(D)
\begin{center}
\begin{tabular}{ | c | c | }
\hline
$x$ & $f ( x )$ \\
\hline
4 & 0 \\
\hline
5 & 0 \\
\hline
7 & 0 \\
\hline
\end{tabular}
\end{center}
(E)
\begin{center}
\begin{tabular}{ | c | c | }
\hline
$x$ & $f ( x )$ \\
\hline
4 & 0 \\
\hline
5 & 4 \\
\hline
7 & 6 \\
\hline
\end{tabular}
\end{center}