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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 \(\displaystyle (-7, 7)\) local min \(\displaystyle (8, -9)\). The function is increasing on \(\displaystyle (-\infty, -7) \cup (8, \infty)\) and decreasing on \(\displaystyle (-7, 8)\).
\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={-9.0}:{10.0}, latex-latex, yscale = 1, samples =350] plot(\x, {0.0094815*(\x)^3 - 0.014222*(\x)^2 - 1.5929*(\x) - 0.20119});
\end{tikzpicture}
\soln{0cm}{The local max $(-7, 7)$ local min $(8, -9)$. The function is increasing on $(-\infty, -7) \cup (8, \infty)$ and decreasing on $(-7, 8)$. }
\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 (-7, 7) " src="/equation_images/%20%5Cdisplaystyle%20%28-7%2C%207%29%20" alt="LaTeX: \displaystyle (-7, 7) " data-equation-content=" \displaystyle (-7, 7) " /> local min <img class="equation_image" title=" \displaystyle (8, -9) " src="/equation_images/%20%5Cdisplaystyle%20%288%2C%20-9%29%20" alt="LaTeX: \displaystyle (8, -9) " data-equation-content=" \displaystyle (8, -9) " /> . The function is increasing on <img class="equation_image" title=" \displaystyle (-\infty, -7) \cup (8, \infty) " src="/equation_images/%20%5Cdisplaystyle%20%28-%5Cinfty%2C%20-7%29%20%5Ccup%20%288%2C%20%5Cinfty%29%20" alt="LaTeX: \displaystyle (-\infty, -7) \cup (8, \infty) " data-equation-content=" \displaystyle (-\infty, -7) \cup (8, \infty) " /> and decreasing on <img class="equation_image" title=" \displaystyle (-7, 8) " src="/equation_images/%20%5Cdisplaystyle%20%28-7%2C%208%29%20" alt="LaTeX: \displaystyle (-7, 8) " data-equation-content=" \displaystyle (-7, 8) " /> . </p> </p>