\begin{frame}
  \frametitle{Derivative as a Function}
  
  \begin{exampleblock}{}
    Where is $f(x) = |x|$ differentiable?
    \pause\medskip
    
    For $x > 0$ we have:
    \begin{itemize}
    \pause
      \item $|x| = x$,
    \pause
      \item $|x+h| = x+h$ for small enough $h$.
    \end{itemize}
    \pause
    Thus for $x > 0$
    \begin{talign}
      f'(x) = \lim_{h\to 0} \frac{f(x+h) - f(x)}{h} 
      \mpause[1]{=  \lim_{h\to 0} \frac{x+h - x}{h}}
      \mpause[2]{= \lim_{h\to 0} 1}
      \mpause[3]{= 1}
    \end{talign}
    \pause\pause\pause\pause
    For $x < 0$ we have:
    \begin{itemize}
    \pause
      \item $|x| = -x$,
    \pause
      \item $|x+h| = -x-h$ for small enough $h$.
    \end{itemize}
    \pause
    Thus for $x < 0$
    \begin{talign}
      f'(x) = \lim_{h\to 0} \frac{f(x+h) - f(x)}{h} 
      \mpause[1]{=  \lim_{h\to 0} \frac{-x-h + x}{h}}
      \mpause[2]{= \lim_{h\to 0} -1}
      \mpause[3]{= -1}
    \end{talign}
  \end{exampleblock}
  \vspace{10cm}
\end{frame}