Let $f$ be the function defined by $f(x) = \cos(2x) + e^{\sin x}$.

Let $g$ be a differentiable function. The table below gives values of $g$ and its derivative $g'$ at selected values of $x$.

\begin{center}
\begin{tabular}{ | r | r | r | }
\hline
\multicolumn{1}{|c|}{$x$} & $g(x)$ & $g'(x)$ \\
\hline\hline
-5 & 10 & -3 \\
\hline
-4 & 5 & -1 \\
\hline
-3 & 2 & 4 \\
\hline
-2 & 3 & 1 \\
\hline
-1 & 1 & -2 \\
\hline
0 & 0 & -3 \\
\hline
\end{tabular}
\end{center}

Let $h$ be the function whose graph, consisting of five line segments, is shown in the figure above.\\
(a) Find the slope of the line tangent to the graph of $f$ at $x = \pi$.\\
(b) Let $k$ be the function defined by $k(x) = h(f(x))$. Find $k'(\pi)$.\\
(c) Let $m$ be the function defined by $m(x) = g(-2x) \cdot h(x)$. Find $m'(2)$.\\
(d) Is there a number $c$ in the closed interval $[-5, -3]$ such that $g'(c) = -4$? Justify your answer.