\begin{frame}
  \frametitle{Derivatives and the Shape of a Graph}

  \begin{exampleblock}{Curve Sketching}
    \begin{malign}
      f(x) = x^4 - 4x^3 = x^3 (x - 4)
      && f'(x) &= 4x^2(x - 3)
    \end{malign}\vspace{-1ex}
    \begin{itemize}
    \pause
      \item $f(x) = 0 \;\iff\;$ \pause \textcolor{cblue}{$x = 0$} \quad or \quad \textcolor{cblue}{$x = 4$}
    \pause
      \item local minimum at \textcolor{cdgreen}{$(3,-27)$} and \textcolor{cdgreen}{$f'(0) = 0$}
    \pause
      \item inflection points \textcolor{cred}{$(0,0)$} and \textcolor{cred}{$(2,-16)$}
    \pause
      \item decreasing on \pause $(-\infty,0)$ and $(0,3)$, \pause increasing on \pause $(3,\infty)$ 
    \pause
      \item concave up on $(-\infty,0)$, down on $(0,2)$, up on $(2,\infty)$
    \end{itemize}
    \pause[1]
    
    \begin{center}
      \scalebox{.7}{
      \begin{tikzpicture}[default,baseline=1cm]
        \diagram{-2.5}{6}{-2}{2}{1}
        \diagramannotatez
        \diagramannotatex{-2,-1,1,2,3,4,5}
        \diagramannotateyy{-1/-16,1/16}
        
        \mpause[2]{ 
          \node[include=cblue,minimum size=4mm] at (0,0) {}; 
          \node[include=cblue] at (4,0) {};
        }
        \mpause[3]{ 
          \node[include=cdgreen] at (3,-27/16) {};
          \node[include=cdgreen,minimum size=3mm] at (0,0) {};
        }
        \mpause[4]{ 
          \node[include=cred] at (0,0) {}; 
          \node[include=cred] at (2,-16/16) {};
        }
        \begin{scope}[ultra thick]
          \mpause[10]{
            \draw[cgreen] plot[smooth,domain=-1.75:0,samples=30] function{(x**4 - 4*x**3)/16};
          }
          \mpause[11]{
            \draw[cgreen] plot[smooth,domain=-0:2,samples=30] function{(x**4 - 4*x**3)/16};
          }
          \mpause[12]{
            \draw[cgreen] plot[smooth,domain=2:3,samples=30] function{(x**4 - 4*x**3)/16};
          }
          \mpause[13]{
            \draw[cgreen] plot[smooth,domain=3:4.35,samples=30] function{(x**4 - 4*x**3)/16};
          }
        \end{scope}
      \end{tikzpicture}
      }
    \end{center}
  \end{exampleblock}
\end{frame}