\begin{frame} \frametitle{Maximum and Minimum Values} \vspace{-1ex} \begin{exampleblock}{} \begin{minipage}{.45\textwidth} The graph of \begin{talign} f(x) = \frac{3x^4 - 16x^3 + 18x^2}{15} \end{talign} for $-1 \le x \le 4$ is shown in this diagram: \end{minipage} \begin{minipage}{.54\textwidth} \begin{center} \scalebox{.7}{ \begin{tikzpicture}[default,baseline=1cm] \diagram{-2}{5}{-2}{3}{1} \diagramannotatey{-1,1,2} \diagramannotatex{-1,1,2,3,4} \diagramannotatez \begin{scope}[cgreen,ultra thick] \draw plot[smooth,domain=-1:4,samples=200] function{(3*x**4 - 16*x**3 + 18*x**2)/15}; \end{scope} \node[cred,include] (a) at (-1,37/15) {}; \node[cred] (b) at ($(a)+(0,.4)$) {1}; \node[cred,include] (a) at (0,0) {}; \node[cred] (b) at ($(a)+(0.15,.4)$) {2}; \node[cred,include] (a) at (1,5/15) {}; \node[cred] (b) at ($(a)+(0,.4)$) {3}; \node[cred,include] (a) at (3,-27/15) {}; \node[cred] (b) at ($(a)+(0,.4)$) {4}; \node[cred,include] (a) at (4,32/15) {}; \node[cred] (b) at ($(a)+(0,.4)$) {5}; \end{tikzpicture} } \end{center} \end{minipage} \pause\smallskip Which of the points are a local / global maxima or minima? \begin{enumerate} \pause \item \noindent\pause global (absolute) maximum;\\ \pause not a local maximum since $f$ is not defined near $-1$ \pause \item \noindent\pause local minimum \pause \item \noindent\pause local maximum \pause \item \noindent\pause global (absolute) and local minimum \pause \item \noindent\pause nothing \end{enumerate} \end{exampleblock} \end{frame}