\begin{frame} \frametitle{Maximum and Minimum Values} \begin{exampleblock}{} Where does \begin{talign} f(x) = x^2 \end{talign} have local / global minima or maxima? \pause\bigskip The value \alert{$f(0) = 0$} is absolute and local minimum since: \begin{talign} f(0) = 0 \le x^2 = f(x) \quad\text{for all $x$} \end{talign} \pause The function has no local or global maxima. \end{exampleblock} \pause \begin{exampleblock}{} \begin{minipage}{.7\textwidth} Where does \begin{talign} f(x) = x^3 \end{talign} have (local or global) minima or maxima? \pause\bigskip The function has no local or global extrema. \end{minipage} \pause \begin{minipage}{.29\textwidth} \scalebox{.6}{ \begin{tikzpicture}[default,baseline=1cm] \diagram{-2}{2}{-2}{2.5}{1} \diagramannotatey{1,2} \diagramannotatex{1,2} \diagramannotatez \begin{scope}[ultra thick] \draw[cgreen,ultra thick] plot[smooth,domain=-1.25:1.35,samples=200] function{x**3}; \end{scope} \end{tikzpicture} } \end{minipage} \end{exampleblock} \end{frame}