2. Consider a function g(x), with domain ($-\infty$, -2) U (-2, 2) U (2, $\infty$). We don't know what
g(x) is, but we are given the sign charts for the first and second derivative of g(x):
\begin{tabular}{|c|c|c|c|c|}
\hline
x & -2 & 0 & 2 & 6 \\
\hline
g'(x) & + & + & - & + \\
\hline
\end{tabular}
\begin{tabular}{|c|c|c|c|}
\hline
x & -5 & -2 & 2 \\
\hline
g''(x) & - & + & + \\
\hline
\end{tabular}
(a) (4 points) On which interval(s) is the function g(x) concave up? Explain how you know.
(b) (4 points) On which interval(s) is the function g(x) decreasing? Explain how you know.
(c) (6 points) Give the x-value(s) of all the extrema of g(x), if any. Classify each one as a
maximum or a minimum. If there are no extrema, explain how you know.
(d) (4 points) Give the x-value(s) of all the inflection points of g(x), if any. If there are no
inflection points, explain how you know.