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Use the graph to find any relative maxima or minima of the function. Find the intervals of which the function is increasing or decreasing.
The local max \(\displaystyle (2, 8)\) local min \(\displaystyle (-8, -9)\). The function is decreasing on \(\displaystyle (-\infty, -8) \cup (2, \infty)\) and increasing on \(\displaystyle (-8, 2)\).
\begin{question}Use the graph to find any relative maxima or minima of the function. Find the intervals of which the function is increasing or decreasing.\newline\begin{tikzpicture}[scale=0.4]
\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}:{4.0}, latex-latex, yscale = 1, samples =350] plot(\x, {-0.034*(\x)^3 - 0.306*(\x)^2 + 1.632*(\x) + 6.232});
\end{tikzpicture}
\soln{0cm}{The local max $(2, 8)$ local min $(-8, -9)$. The function is decreasing on $(-\infty, -8) \cup (2, \infty)$ and increasing on $(-8, 2)$. }
\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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<p> <p>The local max <img class="equation_image" title=" \displaystyle (2, 8) " src="/equation_images/%20%5Cdisplaystyle%20%282%2C%208%29%20" alt="LaTeX: \displaystyle (2, 8) " data-equation-content=" \displaystyle (2, 8) " /> local min <img class="equation_image" title=" \displaystyle (-8, -9) " src="/equation_images/%20%5Cdisplaystyle%20%28-8%2C%20-9%29%20" alt="LaTeX: \displaystyle (-8, -9) " data-equation-content=" \displaystyle (-8, -9) " /> . The function is decreasing on <img class="equation_image" title=" \displaystyle (-\infty, -8) \cup (2, \infty) " src="/equation_images/%20%5Cdisplaystyle%20%28-%5Cinfty%2C%20-8%29%20%5Ccup%20%282%2C%20%5Cinfty%29%20" alt="LaTeX: \displaystyle (-\infty, -8) \cup (2, \infty) " data-equation-content=" \displaystyle (-\infty, -8) \cup (2, \infty) " /> and increasing on <img class="equation_image" title=" \displaystyle (-8, 2) " src="/equation_images/%20%5Cdisplaystyle%20%28-8%2C%202%29%20" alt="LaTeX: \displaystyle (-8, 2) " data-equation-content=" \displaystyle (-8, 2) " /> . </p> </p>