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calculus:resources:calculus_flipped_resources:applications:critical_points_tex

TeX code compiled with \documentclass{beamer} using the Amsterdam theme.

\begin{document} \begin{frame} \large Sketch the graph of $y=(x-1)^2+2$ on the closed interval $[-4,4]$. \vskip 15pt \begin{itemize} \item[\bf (a)] What are the local maximum and minimum values? points? \vskip 15pt \item[\bf (b)] What are the absolute maximum and minimum values? points? \end{itemize} \end{frame} \begin{frame} \large Find the critical number of the following functions \vskip 15pt \begin{itemize} \item[\bf (a)] $f(x) = 8x^3-12x^2-48x$ \vskip 15pt \item[\bf (b)] $g(x) = x^{\frac{3}{4}} - 9x^{\frac{1}{4}}$ \vskip 15pt \item[\bf (c)] $h(\theta) = 18\cos(\theta) + 9\sin^2(\theta)$ \end{itemize} \end{frame} \begin{frame} \large Show that $5$ is a critical number of the function $$g(x)=2+(x-5)^2$$ but $g$ does not have a local extreme value of $5$. \vskip 60pt If $f$ has a minimum value of $c$, does the function $g(x)=-f(x)$ have a maximum value of $c$? \end{frame} \end{document}