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Find all local maximum and minimums of the graph. Approximate as needed.


The graph will have local maximum if it changes from increasing to decreasing and a local minimum if it changes from decreasing to increaing. The graph has a local maximum at \(\displaystyle (1, 7)\). The graph has a local minimum at \(\displaystyle (-5.3,-7.1)\). The point \(\displaystyle (5, -6)\) is neither a local max or local min.

Download Tikz \( \LaTeX \)

\begin{tikzpicture}[scale=.4, font=\Large]
	\draw[very thick, color=blue, opacity=0.3, xstep=1, ystep=1] (-10,-10) grid (10,10);
	\draw[latex-latex, very thick] (-10.4,0)--(10.4,0) node[right]{$x$};
	\draw[latex-latex, very thick] (0,-10.4)--(0,10.4) node[above]{$y$};
	\foreach \x in { -10,-8,...,10 }{
		\pgfmathsetmacro{\xtick}{\x != 0 ? "\x" : ""}
		\draw (\x, .2) -- (\x,-.2) node[below]{$\xtick$};
		}
	\foreach \y in { -10,-8,...,10 }{
		\pgfmathsetmacro{\ytick}{\y != 0 ? "\y" : ""}
		\draw (.2, \y) -- (-.2, \y) node[left]{$\ytick$};
		}
	\draw[thick, color=blue, domain={-10.0}:{1.0}, color=red, very thick,latex-, samples =350] plot(\x, {95*(\x)^2/264 + 333*(\x)/88 + 377/132});
		\draw[very thick, color=red,-latex] (1, 7) -- (5, -6) --(10, -6);
\end{tikzpicture}

Download \(\LaTeX\)

\begin{question}Find all local maximum and minimums of the graph. Approximate as needed.\newline\begin{tikzpicture}[scale=.4, font=\Large]
	\draw[very thick, color=blue, opacity=0.3, xstep=1, ystep=1] (-10,-10) grid (10,10);
	\draw[latex-latex, very thick] (-10.4,0)--(10.4,0) node[right]{$x$};
	\draw[latex-latex, very thick] (0,-10.4)--(0,10.4) node[above]{$y$};
	\foreach \x in { -10,-8,...,10 }{
		\pgfmathsetmacro{\xtick}{\x != 0 ? "\x" : ""}
		\draw (\x, .2) -- (\x,-.2) node[below]{$\xtick$};
		}
	\foreach \y in { -10,-8,...,10 }{
		\pgfmathsetmacro{\ytick}{\y != 0 ? "\y" : ""}
		\draw (.2, \y) -- (-.2, \y) node[left]{$\ytick$};
		}
	\draw[thick, color=blue, domain={-10.0}:{1.0}, color=red, very thick,latex-, samples =350] plot(\x, {95*(\x)^2/264 + 333*(\x)/88 + 377/132});
		\draw[very thick, color=red,-latex] (1, 7) -- (5, -6) --(10, -6);
\end{tikzpicture}

    \soln{0cm}{The graph will have local maximum if it changes from increasing to decreasing and a local minimum if it changes from decreasing to increaing. The graph has a local maximum at $(1, 7)$. The graph has a local minimum at $(-5.3,-7.1)$. The point $(5, -6)$ is neither a local max or local min. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage[margin=2cm]{geometry}
\usepackage{tcolorbox}

\newcounter{ExamNumber}
\newcounter{questioncount}
\stepcounter{questioncount}

\newenvironment{question}{{\noindent\bfseries Question \arabic{questioncount}.}}{\stepcounter{questioncount}}
\renewcommand{\labelenumi}{{\bfseries (\alph{enumi})}}

\newif\ifShowSolution
\newcommand{\soln}[2]{%
\ifShowSolution%
\noindent\begin{tcolorbox}[colframe=blue,title=Solution]#2\end{tcolorbox}\else%
\vspace{#1}%
\fi%
}%
\newcommand{\hideifShowSolution}[1]{%
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%
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\everymath{\displaystyle}
\ShowSolutiontrue

\begin{document}\begin{question}(10pts) The question goes here!
    \soln{9cm}{The solution goes here.}

\end{question}\end{document}
HTML for Canvas
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HTML for Canvas
<p> <p>The graph will have local maximum if it changes from increasing to decreasing and a local minimum if it changes from decreasing to increaing. The graph has a local maximum at  <img class="equation_image" title=" \displaystyle (1, 7) " src="/equation_images/%20%5Cdisplaystyle%20%281%2C%207%29%20" alt="LaTeX:  \displaystyle (1, 7) " data-equation-content=" \displaystyle (1, 7) " /> . The graph has a local minimum at  <img class="equation_image" title=" \displaystyle (-5.3,-7.1) " src="/equation_images/%20%5Cdisplaystyle%20%28-5.3%2C-7.1%29%20" alt="LaTeX:  \displaystyle (-5.3,-7.1) " data-equation-content=" \displaystyle (-5.3,-7.1) " /> . The point  <img class="equation_image" title=" \displaystyle (5, -6) " src="/equation_images/%20%5Cdisplaystyle%20%285%2C%20-6%29%20" alt="LaTeX:  \displaystyle (5, -6) " data-equation-content=" \displaystyle (5, -6) " />  is neither a local max or local min. </p> </p>