\begin{frame}
\frametitle{Review - Midterm Exam 3}
\begin{exampleblock}{}
We consider the function $f(x)$ with
\begin{talign}
f(x) = \frac{1-x^3}{1+x^3}
&&
f'(x) = \frac{6x^2}{(1+x^3)^2}
&&
f''(x) = \frac{12x(2x^3-1)}{(1+x^3)^3}
\end{talign}
\only<-1>{
Find all
\begin{itemize}
\item horizontal, vertical asymptotes,
\item the left and right limits at vertical asymptotes,
\item points with horizontal tangents and local extrema
\item on which intervals is $f$ increasing/decreasing?
\item on which intervals is $f$ concave up/down?
\item inflection points
\end{itemize}
Then sketch the graph of $f(x)$.
}
\only<2>{
\begin{center}
\scalebox{.8}{
\begin{tikzpicture}[default]
\diagram[1]{-5}{5}{-3}{3}{1}
\diagramannotatez
\def\mfunshift{0}
\begin{scope}[ultra thick]
\draw[cgreen] plot[smooth,domain=-5:-1.25,samples=100] function{(1-x**3)/(1+x**3)};
\draw[cgreen] plot[smooth,domain=-.8:5,samples=100] function{(1-x**3)/(1+x**3)};
\end{scope}
\end{tikzpicture}
}
\end{center}
}
\end{exampleblock}
\end{frame}