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Consider the function $f(x)=x^3-2x^2+2x$.
\begin{enumerate}[(a)]
\item Find the local extrema of $f'(x)$.  Are there any absolute extrema of $f'$ on $(-\infty,\infty)$?  Explain your findings.
\item Prove that $f(x)$ is an increasing function.  (How can your work in part (a) help you with your argument?)


\end{enumerate} 
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