\begin{frame}
  \frametitle{Derivatives and the Shape of a Graph}
  
  \begin{block}{}
    If $f'(x) > 0$ on an interval, then $f$ is increasing on that interval. 
    \pause\medskip

    If $f'(x) < 0$ on an interval, then $f$ is decreasing on that interval. 
  \end{block}
  \pause
  
  \begin{exampleblock}{}
    Where is $f(x) = 3x^4 - 4x^3 -12x^2 + 5$ increasing/decreasing?
    \pause
    \begin{talign}
      f'(x) = \mpause[1]{12x^3 - 12x^2 - 24x}
      \mpause[2]{= 12x(x-2)(x+1)}
    \end{talign}
    \pause\pause\pause
    {\small
    \begin{tabular}{|c|c|c|c|c|l|}
      \hline
      Interval & $12x$ & $x-2$ & $x+1$ & $f'(x)$ & \\
      \hline
      \mpause[1]{x < -1} & \mpause[5]{-} & \mpause{-} & \mpause{-} & \mpause{-} & \mpause{decreasing on $(-\infty,-1)$} \\
      \hline
      \mpause[2]{-1 < x < 0} & \mpause[10]{-} & \mpause{-} & \mpause{+} & \mpause{+} & \mpause{increasing on $(-1,0)$} \\
      \hline
      \mpause[3]{0 < x < 2} & \mpause[15]{+} & \mpause{-} & \mpause{+} & \mpause{-} & \mpause{decreasing on $(0,2)$} \\
      \hline
      \mpause[4]{2 < x} & \mpause[20]{+} & \mpause{+} & \mpause{+} & \mpause{+} & \mpause{increasing on $(2,\infty)$} \\
      \hline
    \end{tabular}
    }
    \pause[31]
    \begin{center}\vspace{-1ex}
    \scalebox{.8}{
    \begin{tikzpicture}[default,baseline=1cm]
      \diagram{-2}{4}{-1}{1.3}{1}
      \diagramannotatez
      \diagramannotateyy{-1/-30,1/30}
      \diagramannotatex{-2,-1,1,2,3}
      \begin{scope}[ultra thick]
        \draw[cgreen] plot[smooth,domain=-2:3,samples=30] function{(3*x**4 - 4*x**3 - 12*x**2 + 5)/30};
      \end{scope}
    \end{tikzpicture}\vspace{-1ex}
    }
    \end{center}
  \end{exampleblock}
\end{frame}