\begin{frame} \frametitle{Increasing and Decreasing Functions} \begin{block}{} A function $f$ is \emph{increasing} on an interval $I$ if \begin{talign} f(x_1) < f(x_2) &&\text{whenever $x_1 < x_2$ and $x_1,x_2 \in I$} \end{talign} \pause The function is \emph{decreasing} on an interval $I$ if \begin{talign} f(x_1) > f(x_2) &&\text{whenever $x_1 < x_2$ and $x_1,x_2 \in I$} \end{talign} \end{block} \bigskip\pause \begin{minipage}{.60\textwidth} \scalebox{.75}{ \begin{tikzpicture}[default,baseline=0ex] \diagram{-.5}{7}{-.5}{4}{1} \diagramannotatez \diagramannotatex{1,2,3,4,5,6} \diagramannotatey{1,2,3} \begin{scope}[ultra thick] % \draw[cgreen] plot[smooth,domain=0:2,samples=20] (\x,{pow(\x,3)}); \draw[cgreen] (0,1) to[in=180,out=0] (3,3) to[in=180,out=0,looseness=.5] (4,1.5) to[in=180,out=0,looseness=.5] (6,3.5); \end{scope} \end{tikzpicture} } \end{minipage} \begin{minipage}{.39\textwidth} \pause \ This function is: \begin{itemize} \pause \item increasing on $[0,3]$ \pause\smallskip \item decreasing on $[3,4]$ \pause\smallskip \item increasing on $[4,6]$ \end{itemize} \end{minipage} \end{frame}