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\begin{frame}
\frametitle{Derivatives and the Shape of a Graph}

\begin{block}{First Derivative Test}
Suppose that $c$ is a critical number of a continuous function $f$.\\
\begin{itemize}
\pause
\item If $f'$ changes the sign from positive to negative,\\
then $f$ has a local maximum at $c$.
\pause\smallskip
\item If $f'$ changes the sign from negative to positive,\\
then $f$ has a local minimum at $c$.
\pause\smallskip
\item If $f'$ does not change sign at $c$,\\
then $f$ has no local extremum at $c$.
\end{itemize}
\end{block}
\pause[1]

\begin{center}
\scalebox{.7}{
\pause
\begin{tikzpicture}[default,baseline=1cm]
\diagram{-.5}{3}{-.2}{2.5}{1}
\diagramannotatez
\begin{scope}[ultra thick]
\draw[cgreen] plot[smooth,domain=0:3,samples=30] function{2-(x-1.5)**2};
\tangent{1cm}{1cm}{2-pow(\x-1.5,2)}{0.75}
\tangent{1cm}{1cm}{2-pow(\x-1.5,2)}{2.25}
\end{scope}
\end{tikzpicture}
\begin{tikzpicture}[default,baseline=1cm]
\diagram{-.5}{3}{-.2}{2.5}{1}
\diagramannotatez
\begin{scope}[ultra thick]
\draw[cgreen] plot[smooth,domain=0:3,samples=30] function{(x-1.5)**2};
\tangent{1cm}{1cm}{pow(\x-1.5,2)}{0.75}
\tangent{1cm}{1cm}{pow(\x-1.5,2)}{2.25}
\end{scope}
\end{tikzpicture}