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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 \(\displaystyle (-2, 7)\) local min \(\displaystyle (7, -9)\). The function is increasing on \(\displaystyle (-\infty, -2) \cup (7, \infty)\) and decreasing on \(\displaystyle (-2, 7)\).
\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 }{
\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={-4.0}:{9.0}, latex-latex, yscale = 1, samples =350] plot(\x, {0.043896*(\x)^3 - 0.32922*(\x)^2 - 1.8436*(\x) + 4.9808});
\end{tikzpicture}
\soln{0cm}{The local max $(-2, 7)$ local min $(7, -9)$. The function is increasing on $(-\infty, -2) \cup (7, \infty)$ and decreasing on $(-2, 7)$. }
\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 (-2, 7) " src="/equation_images/%20%5Cdisplaystyle%20%28-2%2C%207%29%20" alt="LaTeX: \displaystyle (-2, 7) " data-equation-content=" \displaystyle (-2, 7) " /> 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, -2) \cup (7, \infty) " src="/equation_images/%20%5Cdisplaystyle%20%28-%5Cinfty%2C%20-2%29%20%5Ccup%20%287%2C%20%5Cinfty%29%20" alt="LaTeX: \displaystyle (-\infty, -2) \cup (7, \infty) " data-equation-content=" \displaystyle (-\infty, -2) \cup (7, \infty) " /> and decreasing on <img class="equation_image" title=" \displaystyle (-2, 7) " src="/equation_images/%20%5Cdisplaystyle%20%28-2%2C%207%29%20" alt="LaTeX: \displaystyle (-2, 7) " data-equation-content=" \displaystyle (-2, 7) " /> . </p> </p>