\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}