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\begin{frame}
\frametitle{Curve Sketching}

\begin{block}{}
For sketching a curve of $f(x)$:
\begin{itemize}
\pause
\item determine the \emph{domain}
\pause
\item find the \emph{$y$-intercept} $f(0)$ and the \emph{$x$-intercepts} $f(x) = 0$
\pause
\item find \emph{vertical asymptotes $x = a$}, that is:\vspace{-1ex}
\begin{talign}
\lim_{x\to a^-} = \pm\infty &&\text{ or }&& \lim_{x\to a^+} = \pm\infty
\end{talign} \vspace{-2ex}
\pause
\item find \emph{horizontal asymptotes $y = L$}, that is:\vspace{-1ex}
\begin{talign}
\lim_{x\to \infty} = L &&\text{ or }&& \lim_{x\to -\infty} = L
\end{talign} \vspace{-2ex}
\pause
\item find intervals of \emph{increase} $f'(x) > 0$ and \emph{decrease} $f'(x) < 0$
\pause
\item find \emph{local maxima and minima}
\pause
\item determine \emph{concavity} on intervals and \emph{points of inflection}
\begin{itemize}
\item $f''(x) > 0$ concave upward
\item $f''(x) < 0$ concave downward
\item inflections points where $f''(x)$ changes the sign
\end{itemize}
\end{itemize}
\end{block}
\end{frame}