\begin{frame}
  \frametitle{Mean Value Theorem}

  \meanvalueshort
  \bigskip
  
  Important consequences of the Mean Value Theorem are:
  \pause 
  \begin{block}{}
    If $f'(x) = 0$ for all $x$ in $(a,b)$ then $f$ is constant on $(a,b)$.
  \end{block}
  \pause
  (Proof like the previous example)
  \pause\medskip

  \begin{block}{}
    If $f'(x) = g'(x)$ for all $x$ in $(a,b)$ then $f-g$ is constant on $(a,b)$.
  \end{block}
  \pause
  (In other words, then $f(x) = g(x) + k$ for a constant $k$) 
  \pause
  
  \begin{proof}
    \pause
    Let $h = f - g$. \pause Then $h' = f' - g' \pause = 0$ on $(a,b)$. \pause 
    Thus $h$ is constant on $(a,b)$.
  \end{proof}
  \vspace{10cm}
\end{frame}