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\begin{frame}
\frametitle{Optimization}

The argument we have used on the last slide is the following:
\bigskip
\begin{block}{First Derivative Test for Absolute Extreme Values}
Let $f$ be continuous, defined on an open or closed interval.\\
Let $c$ be a critical number of $f$.
\begin{itemize}
\medskip
\item If $f'(x) > 0$ for all $x < c$, and $f'(x) < 0$ for all $x > c$,\\
then $f(c)$ is the absolute maximum of $f$.
\medskip
\item If $f'(x) < 0$ for all $x < c$, and $f'(x) > 0$ for all $x > c$,\\
then $f(c)$ is the absolute minimum of $f$.
\end{itemize}
\end{block}
\end{frame}