\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}