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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 \(\displaystyle (-5.6,7.00)\). The graph has a local minimum at \(\displaystyle (0, -9)\). The point \(\displaystyle (3, 4)\) is neither a local max or local min.
\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" : ""}
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}
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}
\draw[thick, color=blue, domain={-10.0}:{0.0}, color=red, very thick,latex-, samples =350] plot(\x, {-18*(\x)^2/35 - 201*(\x)/35 - 9});
\draw[very thick, color=red,-latex] (0, -9) -- (3, 4) --(10, 4);
\end{tikzpicture}
\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}:{0.0}, color=red, very thick,latex-, samples =350] plot(\x, {-18*(\x)^2/35 - 201*(\x)/35 - 9});
\draw[very thick, color=red,-latex] (0, -9) -- (3, 4) --(10, 4);
\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 $(-5.6,7.00)$. The graph has a local minimum at $(0, -9)$. The point $(3, 4)$ is neither a local max or local min. }
\end{question}
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\begin{document}\begin{question}(10pts) The question goes here!
\soln{9cm}{The solution goes here.}
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<path style="fill:none;stroke-width:1.19553;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(100%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 0.00159375 -102.047875 L 34.017219 45.354469 L 107.646125 45.354469 " transform="matrix(1,0,0,-1,129.307,134.124)"/>
<path style=" stroke:none;fill-rule:nonzero;fill:rgb(100%,0%,0%);fill-opacity:1;" d="M 242.691406 88.769531 C 240.992188 88.449219 238.230469 87.496094 236.316406 86.378906 L 236.316406 91.160156 C 238.230469 90.046875 240.992188 89.089844 242.691406 88.769531 "/>
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<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 (-5.6,7.00) " src="/equation_images/%20%5Cdisplaystyle%20%28-5.6%2C7.00%29%20" alt="LaTeX: \displaystyle (-5.6,7.00) " data-equation-content=" \displaystyle (-5.6,7.00) " /> . The graph has a local minimum at <img class="equation_image" title=" \displaystyle (0, -9) " src="/equation_images/%20%5Cdisplaystyle%20%280%2C%20-9%29%20" alt="LaTeX: \displaystyle (0, -9) " data-equation-content=" \displaystyle (0, -9) " /> . The point <img class="equation_image" title=" \displaystyle (3, 4) " src="/equation_images/%20%5Cdisplaystyle%20%283%2C%204%29%20" alt="LaTeX: \displaystyle (3, 4) " data-equation-content=" \displaystyle (3, 4) " /> is neither a local max or local min. </p> </p>