Welcome to Bytelearn!

Let’s check out your problem:

$11$. A function $f$ is continuous on the closed interval $[4,6]$ and twice differentiable on the open interval $(4,6)$. If $f^{\prime}(5)=-3$, and $f$ is concave downwards on the given interval, which of the following could be a table of values for $f$ ?$\newline$(A)$\newline$\begin{tabular}{|c|c|}$\newline$\hline$x$ & $f(x)$ \\$\newline$\hline $4$ & $8$ \\$\newline$\hline $5$ & $4$ \\$\newline$\hline $6$ & $0$ \\$\newline$\hline$\newline$\end{tabular}$\newline$(B)$\newline$\begin{tabular}{|c|c|}$\newline$\hline$x$ & $f(x)$ \\$\newline$\hline $4$ & $8$ \\$\newline$\hline $5$ & $6$ \\$\newline$\hline $6$ & $2$ \\$\newline$\hline$\newline$\end{tabular}$\newline$(C)$\newline$\begin{tabular}{|c|c|}$\newline$\hline$x$ & $f(x)$ \\$\newline$\hline $4$ & $8$ \\$\newline$\hline $5$ & $6$ \\$\newline$\hline $6$ & $5$ \\$\newline$\hline$\newline$\end{tabular}$\newline$(D)$\newline$\begin{tabular}{|c|c|}$\newline$\hline$x$ & $f(x)$ \\$\newline$\hline $4$ & $8$ \\$\newline$\hline $5$ & $3$ \\$\newline$\hline $6$ & $2$ \\$\newline$\hline$\newline$\end{tabular}