\begin{frame}
  \frametitle{Rates of Change}

  \begin{exampleblock}{}
    A manufacturer produces some fabric.
    The costs for producing $x$ yards are $f(x)$ dollars.
    
    \begin{itemize}
    \pause
      \item What is the meaning of $f'(x)$ (called \emph{marginal costs})?
    \pause
      \item What does it mean to say $f'(1000) = 9$?
    \pause
      \item Which do you think is greater $f'(50)$ or $f'(500)$?
    \end{itemize}
    \pause
    Answers:
    \begin{itemize}
    \pause
      \item $f'(x)$ is the rate of change of production costs in dollars per yard
            with respect to the number of yards produced
    \pause
      \item $f'(1000) = 9$ means that after having produced $1000$ yards,
            the costs increase by $9$ dollars for additional yards
    \pause
      \item Typically $f'(500) < f'(50)$ since usually the cost of production per yard will decrease the more
            you produce (due to fixed costs: you have already bought and installed the machines\ldots)
    \end{itemize}
  \end{exampleblock}
\end{frame}