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Activity 3.3.2 .
Suppose that \(g(x)\) is a function whose first derivative is
\begin{equation*}
g'(x) = \frac{(x+4)(x-2)}{x^2+1}\text{.}
\end{equation*}
(a) Determine, with justification, all critical numbers of
\(g\text{.}\)
(b) By developing a carefully labeled first derivative sign chart, decide whether
\(g\) has as a local maximum, local minimum, or neither at each critical number.
(c) Does
\(g\) have a global maximum? global minimum? Justify your claims.
(d) Sketch a possible graph of
\(y = g(x)\text{.}\) Clearly label any local or global extrema on the graph.
