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

  Let $f$ be a function, and $[a,b]$ a closed interval. Then $f(c)$ is an
  \begin{itemize}
  \pause
    \item \emph{absolute maximum} on $[a,b]$ if $f(c) \ge f(x)$ for all $x$ in~$[a,b]$
  \pause
    \item \emph{absolute minimum} on $[a,b]$ if $f(c) \le f(x)$ for all $x$ in $[a,b]$
  \end{itemize}
  \pause\medskip
  
  \extremevalue
  \pause\medskip

  \begin{exampleblock}{}
  \begin{minipage}{.6\textwidth}
  \begin{center}
  \scalebox{.6}{
  \begin{tikzpicture}[default,baseline=1cm]
    \diagram{-.5}{8}{-.5}{4}{1}
    \diagramannotatey{1,2,3}
    \diagramannotatex{1,2,3,4,5,6,7}
    \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};
      \draw (1,2) to[out=45,in=180] (2,3) to[out=0,in=180] (4,1) to[out=0,in=180] (6,3) to[out=0,in=135] (7,2); 
      \node[include] at (1,2) {};
      \node[include] at (7,2) {};
    \end{scope}
  \end{tikzpicture}
  }
  \end{center}
  \end{minipage}
  \begin{minipage}{.39\textwidth}
    \pause
    Continuous on $[1,7]$.
    \pause\medskip

    Absolute minimum:\\\pause
    $f(4) = 1$
    \pause\medskip
    
    Absolute maximum:\\\pause
    $f(2) = 3$, and\\
    $f(6) = 3$
  \end{minipage}
  \end{exampleblock}
\end{frame}