The functions $f$ and $g$ are twice differentiable. The table shown gives values of the functions and their first derivatives at selected values of $x$.

\begin{center}
\begin{tabular}{ | c | | c | c | c | c | }
\hline
$x$ & 0 & 2 & 4 & 7 \\
\hline\hline
$f(x)$ & 10 & 7 & 4 & 5 \\
\hline
$f'(x)$ & $\frac{3}{2}$ & $-8$ & 3 & 6 \\
\hline
$g(x)$ & 1 & 2 & $-3$ & 0 \\
\hline
$g'(x)$ & 5 & 4 & 2 & 8 \\
\hline
\end{tabular}
\end{center}

(a) Let $h$ be the function defined by $h(x) = f(g(x))$. Find $h'(7)$. Show the work that leads to your answer.

(b) Let $k$ be a differentiable function such that $k'(x) = (f(x))^{2} \cdot g(x)$. Is the graph of $k$ concave up or concave down at the point where $x = 4$? Give a reason for your answer.

(c) Let $m$ be the function defined by $m(x) = 5x^{3} + \int_{0}^{x} f'(t)\, dt$. Find $m(2)$. Show the work that leads to your answer.

(d) Is the function $m$ defined in part (c) increasing, decreasing, or neither at $x = 2$? Justify your answer.