24/116
\begin{frame}
\frametitle{Derivative as a Function}

Which of these functions is the derivative of the other?
\medskip
\begin{center}
\scalebox{.8}{
\begin{tikzpicture}[default,baseline=1cm]
\diagram{-2.5}{2.5}{-2.5}{2.5}{1}
\diagramannotatez
\diagramannotatex{-2,-1,1,2}
\diagramannotatey{-2,-1,1,2}
\begin{scope}[ultra thick]
\draw[cgreen,ultra thick] plot[smooth,domain=-1.6:1.6,samples=20] function{x**3 - x};
\end{scope}
\begin{tikzpicture}[default,baseline=1cm]
\diagram{-2.5}{2.5}{-2.5}{2.5}{1}
\diagramannotatez
\diagramannotatex{-2,-1,1,2}
\diagramannotatey{-2,-1,1,2}
\begin{scope}[ultra thick]
\draw[cred,ultra thick] plot[smooth,domain=-1.3:1.3,samples=20] function{2*x**2 - 1};
\end{scope}
\end{tikzpicture}
}
\end{center}
\pause\medskip
The right is the derivative of the left:
\begin{itemize}
\pause
\item look at local maxima and minima of $f$; then $f'$ must be $0$
\pause
\item where $f$ increases, $f'$ must be positive
\pause
\item where $f$ decreases, $f'$ must be negative
\end{itemize}
\end{frame}