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\begin{frame}
\frametitle{Maximum and Minimum Values}

\vspace{-1ex}
\begin{exampleblock}{}
\begin{minipage}{.45\textwidth}
The graph of
\begin{talign}
f(x) = \frac{3x^4 - 16x^3 + 18x^2}{15}
\end{talign}
for $-1 \le x \le 4$
is shown in this diagram:
\end{minipage}
\begin{minipage}{.54\textwidth}
\begin{center}
\scalebox{.7}{
\begin{tikzpicture}[default,baseline=1cm]
\diagram{-2}{5}{-2}{3}{1}
\diagramannotatey{-1,1,2}
\diagramannotatex{-1,1,2,3,4}
\diagramannotatez
\begin{scope}[cgreen,ultra thick]
\draw plot[smooth,domain=-1:4,samples=200] function{(3*x**4 - 16*x**3 + 18*x**2)/15};
\end{scope}
\node[cred,include] (a) at (-1,37/15) {};
\node[cred] (b) at ($(a)+(0,.4)$) {1};
\node[cred,include] (a) at (0,0) {};
\node[cred] (b) at ($(a)+(0.15,.4)$) {2};
\node[cred,include] (a) at (1,5/15) {};
\node[cred] (b) at ($(a)+(0,.4)$) {3};
\node[cred,include] (a) at (3,-27/15) {};
\node[cred] (b) at ($(a)+(0,.4)$) {4};
\node[cred,include] (a) at (4,32/15) {};
\node[cred] (b) at ($(a)+(0,.4)$) {5};
\end{tikzpicture}
}
\end{center}
\end{minipage}
\pause\smallskip

Which of the points are a local / global maxima or minima?
\begin{enumerate}
\pause
\item \noindent\pause global (absolute) maximum;\\
\pause not a local maximum since $f$ is not defined near $-1$
\pause
\item \noindent\pause local minimum
\pause
\item \noindent\pause local maximum
\pause
\item \noindent\pause global (absolute) and local minimum
\pause
\item \noindent\pause nothing
\end{enumerate}
\end{exampleblock}
\end{frame}