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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 \(\displaystyle (-1, 6)\) local min \(\displaystyle (7, -9)\). The function is increasing on \(\displaystyle (-\infty, -1) \cup (7, \infty)\) and decreasing on \(\displaystyle (-1, 7)\).
\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);
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\foreach \x in { -10,-8,...,10 }{
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\draw (.2, \y) -- (-.2, \y) node[left]{$\ytick$};
}
\draw[thick, color=blue, domain={-3.0}:{9.0}, latex-latex, yscale = 1, samples =350] plot(\x, {0.058594*(\x)^3 - 0.52734*(\x)^2 - 1.2305*(\x) + 5.3555});
\end{tikzpicture}
\soln{0cm}{The local max $(-1, 6)$ local min $(7, -9)$. The function is increasing on $(-\infty, -1) \cup (7, \infty)$ and decreasing on $(-1, 7)$. }
\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 (-1, 6) " src="/equation_images/%20%5Cdisplaystyle%20%28-1%2C%206%29%20" alt="LaTeX: \displaystyle (-1, 6) " data-equation-content=" \displaystyle (-1, 6) " /> local min <img class="equation_image" title=" \displaystyle (7, -9) " src="/equation_images/%20%5Cdisplaystyle%20%287%2C%20-9%29%20" alt="LaTeX: \displaystyle (7, -9) " data-equation-content=" \displaystyle (7, -9) " /> . The function is increasing on <img class="equation_image" title=" \displaystyle (-\infty, -1) \cup (7, \infty) " src="/equation_images/%20%5Cdisplaystyle%20%28-%5Cinfty%2C%20-1%29%20%5Ccup%20%287%2C%20%5Cinfty%29%20" alt="LaTeX: \displaystyle (-\infty, -1) \cup (7, \infty) " data-equation-content=" \displaystyle (-\infty, -1) \cup (7, \infty) " /> and decreasing on <img class="equation_image" title=" \displaystyle (-1, 7) " src="/equation_images/%20%5Cdisplaystyle%20%28-1%2C%207%29%20" alt="LaTeX: \displaystyle (-1, 7) " data-equation-content=" \displaystyle (-1, 7) " /> . </p> </p>