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Questions: Algebra BusinessCalculus
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Draw/sketch the end behavior that best describes \begin{equation*}f(x) = - 6 x^{4} - 12 x^{3} + 25 x^{2} + 70\end{equation*}
The coefficient is \(\displaystyle a_n=-6\) and is negative. The degree is \(\displaystyle 4\) and is even. So the end behavior is
\begin{tikzpicture}
\draw[-latex,domain=0:-1] plot ({\x-.25},{-1*\x*\x});
\draw[-latex,domain=0:1] plot ({\x+.25},{-1*\x*\x});%neg even
\end{tikzpicture}
\begin{question}Draw/sketch the end behavior that best describes
\begin{equation*}f(x) = - 6 x^{4} - 12 x^{3} + 25 x^{2} + 70\end{equation*}
\soln{5cm}{The coefficient is $a_n=-6$ and is negative. The degree is $4$ and is even. So the end behavior is
\begin{tikzpicture}
\draw[-latex,domain=0:-1] plot ({\x-.25},{-1*\x*\x});
\draw[-latex,domain=0:1] plot ({\x+.25},{-1*\x*\x});%neg even
\end{tikzpicture}
}
\end{question}
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\everymath{\displaystyle}
\ShowSolutiontrue
\begin{document}\begin{question}(10pts) The question goes here!
\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Draw/sketch the end behavior that best describes
<img class="equation_image" title=" f(x) = - 6 x^{4} - 12 x^{3} + 25 x^{2} + 70 " src="/equation_images/%20f%28x%29%20%3D%20-%206%20x%5E%7B4%7D%20-%2012%20x%5E%7B3%7D%20%2B%2025%20x%5E%7B2%7D%20%2B%2070%20" alt="LaTeX: f(x) = - 6 x^{4} - 12 x^{3} + 25 x^{2} + 70 " data-equation-content=" f(x) = - 6 x^{4} - 12 x^{3} + 25 x^{2} + 70 " /> </p> </p><p> <p>The coefficient is <img class="equation_image" title=" \displaystyle a_n=-6 " src="/equation_images/%20%5Cdisplaystyle%20a_n%3D-6%20" alt="LaTeX: \displaystyle a_n=-6 " data-equation-content=" \displaystyle a_n=-6 " /> and is negative. The degree is <img class="equation_image" title=" \displaystyle 4 " src="/equation_images/%20%5Cdisplaystyle%204%20" alt="LaTeX: \displaystyle 4 " data-equation-content=" \displaystyle 4 " /> and is even. So the end behavior is
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