\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

  The theorem suggests where local extra can occur:
  \begin{itemize}
  \pause
    \item where $f'(c) = 0$, or
  \pause
    \item where $f'(c)$ does not exist.
  \end{itemize}
  \pause
  
  \begin{block}{}
    A \emph{critical number} of a function $f$ is a number $c$ in the domain of $f$
    such that either $f'(c) = 0$, or $f'(c)$ does not exist.
  \end{block}
  \pause
  
  \begin{exampleblock}{}
    What are the critical numbers of $f(x) = x^{3/5}(5-x)$?
    \pause
    \begin{talign}
      &f(x) = x^{3/5}(5-x) \mpause[1]{= 5x^{3/5} - x^{8/5}} \\
      &\mpause[2]{f'(x) = }
      \mpause[3]{\frac{3}{x^{2/5}} - \frac{8}{5}x^{3/5}} 
      \mpause[4]{= \frac{15}{5x^{2/5}} - \frac{8x}{5x^{2/5}}} 
      \mpause[5]{= \frac{15 - 8x}{5x^{2/5}}} 
    \end{talign}
    \pause\pause\pause\pause\pause\pause
    The critical numbers are $\frac{15}{8}$ ($f(c) = 0$) and $0$ ($f(c)$ does not exist)\hspace{-5ex}
  \end{exampleblock}
  \vspace{10cm}
\end{frame}