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\noindent  {   \bfseries Sketch of a graph }\\


\begin{enumerate}



%%1%%
\item [1.] Let $f(x) = x^3 - 6x^2 + 9x +1 $.
\\
(1) Find the intervals where $f$ is increasing and the intervals
where $f$ is decreasing.\\
(2) Find the local maximum point and the local minimum point of
$f$.
\\
(3) Find the intervals where $f$ is concave up and the
           intervals where $f$ is concave down.
\\
(4) Find the inflection point of $f$.
\\
(5) Sketch $f$.
\\

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\

%%2%%
\item [2.] Let $f(x) =\displaystyle \frac{x^2- 3}{x^3} $.
\\
(1) Find the asymptote of $f$.
\\
(2) Find the $x$-intercepts and $y$-intercepts of $f$.
\\
(3) Show that $f$ is an odd function.
\\
(4) Find the intervals where $f$ is increasing and the intervals
 where $f$ is decreasing.
\\
(5) Find the local maximum point and the local minimum point of
$f$.
\\
(6) Find the intervals where $f$ is concave up and the
           intervals where $f$ is concave down.\\
(7) Find the inflection points of $f$.
\\
(8) Sketch $f$.


 \




\end{enumerate}

\end{document}
