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\textbf{Math 220 \hfill Quiz 8 (take-home) \hfill Fall 2011} \\
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\textbf{Name}\ \rule{3.5in}{.4pt}
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\begin{itemize}
\item You may work with other students in this class. However each student should write up solutions separately and independently -- nobody should copy someone else's work.
\item You may use your notes or the textbook.
\item Computers are not allowed on any problem. You may use a calculator only for basic arithmetic.
\item You must show sufficient work to justify each answer.
\item The quiz should be turned in to your TA at the beginning of your discussion section meeting on Thursday, October 13th.
\item Be sure that the pages are nicely stapled -- do not just fold the corners.
\item \textbf{Note to TAs and Tutors -- you should not help students with these specific problems or go over solutions until after 4pm Thursday.}
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\item (3 points) Determine the $x$-value for each inflection point on the graph of the following function.
$$f(x) = 3x^5 - 5x^4 - 80x^3 + 360x^2 + 1000x + 850$$
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\item (3 points) Suppose the function $f$ has first derivative as shown below.
$$f'(x) = e^{2x}\left(x^2 + 25\right)\left(x-3\right)^2\left(x^2 - 64\right)\left(2x - 1\right)$$
List each interval upon which the function $f$ is decreasing.
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\item (4 points) A farmer wishes to enclose a rectangular pen with area 100 square feet next to a road. The fence along the road is to be reinforced and costs $\$34$ per foot. Fencing that costs $\$16$ per foot can be used for the other three sides. What dimensions for the pen will minimize the cost to the farmer? What is that minimum cost?
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