\begin{frame} \frametitle{Maximum and Minimum Values} \begin{center}\vspace{-2ex} \scalebox{.85}{ \begin{tikzpicture}[default,baseline=1cm] \def\diay{} \diagram{-1}{5}{-.5}{3.5}{1} \diagramannotatez \def\xa{.5} \def\xb{1.5} \def\xc{2.5} \def\xd{3} \def\xe{4} \def\xf{4.5} \begin{scope}[gray] \draw (\xa,1) -- node[black,at end,below] {$a$} (\xa,-.2); \draw (\xb,2.5) -- node[black,at end,below] {$b$} (\xb,-.2); \draw (\xc,2.8) -- node[black,at end,below] {$c$} (\xc,-.2); \draw (\xd,1.5) -- node[black,at end,below] {$d$} (\xd,-.2); \draw (\xe,3.5) -- node[black,at end,below] {$e$} (\xe,-.2); \draw (\xf,1.5) -- node[black,at end,below] {$f$} (\xf,-.2); \end{scope} \begin{scope}[cgreen,ultra thick] \draw (\xa,1) to[out=80,in=220] node[include,at start] {} node[include,at end] {} (\xb,2.5); \draw (\xb,1.5) to[out=80,in=200] node[exclude,at start] {} node[exclude,at end] {} (\xc,2.8); \draw (\xc,2) to[out=-70,in=180] node[include,at start] {} (\xd,1.5) to[out=0,in=-90,looseness=.5] (\xe,3.5) to[out=-90,in=120,looseness=.5] node[include,at end] {} (\xf,1.5); \end{scope} \end{tikzpicture} } \end{center} Which of the points are global/local maxima/minima? \begin{itemize} \pause \item [$a$] \ \pause global (absolute) minimum, but not a local minimum \pause \item [$b$] \ \pause local maximum \pause \item [$c$] \ \pause nothing \pause \item [$d$] \ \pause local minimum \pause \item [$e$] \ \pause local and global (absolute) maximum \pause \item [$f$] \ \pause nothing \end{itemize} \end{frame}