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{\Large Extra Credit} - 10 points possible

This is due in my hands no later then the beginning of class Wednesday, July 31.

Show all relevant work.
Make your work neat, 
I will take off points if I cannot easily read your answers.
All are worth one point except number~\ref{graph} which is worth four.

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Consider the function:
\[
f(x)=\frac{x^3-8x^2+5x+4}{x^3-1}
\]

\begin{enumerate}

\item  Find the domain of $f$.

\item  Find the intervals where $f$ is increasing and decreasing.

\item  Find all local maxima and minima.  (Remember to test critical points)

\item  Find the intervals where $f$ is concave up and concave down.

\item  Find all infection points of $f$.  (Remember to test if it is an inflection point)

\item  Find all asymptotes of $f$.

\item  \label{graph}  Sketch the graph of $f$.  Label local extrema, inflection points, asymptotes.

\end{enumerate}



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