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

  \begin{block}{Summary: Finding Local Extrema}
    \pause
    Find critical numbers $c$: $f'(c) = 0$ or $f'(c)$ does not exist.
    \pause\medskip
    
    First \emph{Derivative Test} ($f$ needs to be continuous at $c$):
    \begin{itemize}
    \pause
      \item If $f'$ changes from $+$ to $-$ at $c$ $\implies$ local maximum
    \pause
      \item If $f'$ changes from $-$ to $+$ at $c$ $\implies$ local minimum
    \pause
      \item If $f'$ does not change sign at $c$  $\implies$ no local extremum
    \end{itemize}
    \pause\medskip

    The \emph{Second Derivative Test}:
    \begin{enumerate}
    \pause
      \item $f'(c) = 0$ and $f''(c) > 0$ $\implies$ local minimum
    \pause
      \item $f'(c) = 0$ and $f''(c) < 0$ $\implies$ local maximum
    \pause
      \item $f'(c)$ or $f''(c)$ does not exist or $f''(c) = 0$\\ $\implies$ use the First Derivative Test
    \end{enumerate}    
  \end{block}
\end{frame}