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

  \begin{block}{Fermat's Theorem}
    \alert{If} $f$ has a local maximum or minimum at $c$ and $f'(c)$ exists, \\
    \alert{then} $f'(c) = 0$.
  \end{block}
  \pause\bigskip

  We can now rephrase the the theorem as follows:
  \begin{block}{}
    If $f$ has a local extremum at $c$, then $c$ is a critical number of $f$.
  \end{block}
  \pause\bigskip
  
  We can use this to look for global extrema on intervals:
  \begin{block}{Closed Interval Method}
    To find the \emph{absolute} maximum and minimum values of a \alert{continuous} function $f$ 
    on an \alert{closed} interval $[a,b]$:
    \begin{enumerate}
    \pause
      \item Find the values of $f$ at critical numbers of $f$ in $(a,b)$.
    \pause
      \item Find the values of $f$ at the endpoints of the interval.
    \pause
      \item The largest value of (1) and (2) is the absolute maximum, the lowest the absolute minimum.
    \end{enumerate}
  \end{block}
  \vspace{10cm}
\end{frame}