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\begin{frame}
\frametitle{Slant Asymptotes}

\begin{exampleblock}{}
Sketch the graph of $f(x) = \frac{x^3}{2x^2+1}$.
\vspace{-1ex}

\begin{overlayarea}{\textwidth}{2cm}
\begin{itemize}
\only<1-3> {
\item $x$- and $y$-intercept: \quad $(0,0)$
}
\only<2-3> {
\item inflection points: $(-\sqrt{\frac{3}{2}},-\frac{3}{8}\sqrt{\frac{3}{2}})$, $(0,0)$ and $(\sqrt{\frac{3}{2}},\frac{3}{8}\sqrt{\frac{3}{2}})$
}
\only<3-3> {
\item slant asymptote: \quad $y = \frac{1}{2}x$
}
\only<4-> {
\item increasing on $(-\infty,\infty)$ and $f'(0) = 0$
\item concave up on $(-\infty,-\sqrt{3/2})$ and $(0,\sqrt{3/2})$
\item concave down on $(-\sqrt{3/2},0)$ and $(\sqrt{3/2},\infty)$
}
\end{itemize}
\end{overlayarea}\vspace{-1ex}

\begin{center}
\scalebox{.7}{
\begin{tikzpicture}[default,baseline=1cm,yscale=1.75]
{\def\diabordery{.25cm}
\diagram{-4}{4}{-2}{2}{1}}
\diagramannotatez
\diagramannotatex{-2,-1,1,2}
\diagramannotatey{-1,1}

\node[include=cred,minimum size=3mm] at (0,0) {};
\pause
\node[include=cgreen] at ({-pow(3/2,.5)},{-3/8*pow(3/2,.5)}) {};
\node[include=cgreen] at (0,0) {};
\node[include=cgreen] at ({pow(3/2,.5)},{3/8*pow(3/2,.5)}) {};
\pause
\draw[red,dashed] (-4,-2) -- (4,2);
\pause\pause
\begin{scope}[ultra thick]
\draw[cgreen,ultra thick] plot[smooth,domain=-4:0,samples=200] function{x**3/(2*x**2+1)};
\pause
\draw[cgreen,ultra thick] plot[smooth,domain=0:4,samples=200] function{x**3/(2*x**2+1)};
\end{scope}
\end{tikzpicture}
}
\end{center}
\end{exampleblock}
\vspace{10cm}
\end{frame}