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\begin{frame}
\frametitle{Curve Sketching}

\begin{block}{}
For local minima and maxima:
\begin{itemize}
\pause
\item find critical numbers $c$
\pause
\item then the first First Derivative Test:
\begin{itemize}
\item $f'$ changes from $+$ to $-$ at $c$ $\;\implies\;$ maximum
\item $f'$ changes from $-$ to $+$ at $c$ $\;\implies\;$ minimum
\end{itemize}
\pause
\item Second Derivative Test:
\begin{itemize}
\item $f''(c) < 0$ $\;\implies\;$ maximum
\item $f''(c) > 0$ $\;\implies\;$ minimum
\item $f''(c) = 0$ $\;\implies\;$ use First Derivative Test
\end{itemize}
\end{itemize}
\end{block}
\pause\medskip

\begin{exampleblock}{}
Then sketch the curve:
\begin{itemize}
\pause
\item draw asymptotes as thin dashed lines
\pause
\item mark intercepts, local extrema and inflection points
\pause
\item draw the curve taking into account:
\begin{itemize}
\item increase / decrease, concavity and asymptotes
\end{itemize}
\end{itemize}
\end{exampleblock}
\end{frame}