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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 \(\displaystyle (-4, 9)\) local min \(\displaystyle (4, -5)\). The function is increasing on \(\displaystyle (-\infty, -4) \cup (4, \infty)\) and decreasing on \(\displaystyle (-4, 4)\).
\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={-6.0}:{6.0}, latex-latex, yscale = 1, samples =350] plot(\x, {0.054688*(\x)^3 - 2.625*(\x) + 2.0});
\end{tikzpicture}
\soln{0cm}{The local max $(-4, 9)$ local min $(4, -5)$. The function is increasing on $(-\infty, -4) \cup (4, \infty)$ and decreasing on $(-4, 4)$. }
\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 (-4, 9) " src="/equation_images/%20%5Cdisplaystyle%20%28-4%2C%209%29%20" alt="LaTeX: \displaystyle (-4, 9) " data-equation-content=" \displaystyle (-4, 9) " /> local min <img class="equation_image" title=" \displaystyle (4, -5) " src="/equation_images/%20%5Cdisplaystyle%20%284%2C%20-5%29%20" alt="LaTeX: \displaystyle (4, -5) " data-equation-content=" \displaystyle (4, -5) " /> . The function is increasing on <img class="equation_image" title=" \displaystyle (-\infty, -4) \cup (4, \infty) " src="/equation_images/%20%5Cdisplaystyle%20%28-%5Cinfty%2C%20-4%29%20%5Ccup%20%284%2C%20%5Cinfty%29%20" alt="LaTeX: \displaystyle (-\infty, -4) \cup (4, \infty) " data-equation-content=" \displaystyle (-\infty, -4) \cup (4, \infty) " /> and decreasing on <img class="equation_image" title=" \displaystyle (-4, 4) " src="/equation_images/%20%5Cdisplaystyle%20%28-4%2C%204%29%20" alt="LaTeX: \displaystyle (-4, 4) " data-equation-content=" \displaystyle (-4, 4) " /> . </p> </p>