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\title[Problem Set 4]{Problem Set 4.  Due Monday 11 September}

\begin{document}

\maketitle



\centerline{\sc Problem Set 3.  Problems from Lecture 3.}

\noindent {\bf Reading.} {\em Quick Calculus}, pp. 129--137; 143-150.

\noindent {\bf Supplementary reading.} Simmons, Sections 4.1--4.4..

\begin{enumerate}

\item (10pts) This is a review of some of the differentiation rules from
lecture on Wednesday. Differentiate the following functions.

\begin{enumerate}
\item $y=[\cos(x)\sin(x)]^5$
\item $y=\log_5[(2x^2-6)\cdot(x+7)]$
\item $y=\ln[\cos(4x^2)]$
\item $y=e^{\tan(x)}$
\item $y=\sin(\frac{1}{x})$
\end{enumerate}

\item (6pts) Use the first and second derivatives to graph the
following functions.

\begin{enumerate}
\item $y=x^3+x^2+5x+4$
\item $y=e^{x^2}$
\item $y=\frac{x-3}{x^3-3x^2-9x+27}$
\end{enumerate}


\item (2pts) A university bookstore can get the book {\em The Beer-Lover's
Guide to Boston} at a cost of \$6 per copy from the
publisher.  The bookstore manager estimates that she can sell 180
copies at a price of \$16, and that each \$1 reduction in price will
increase sales by 30 copies.  What should the price of the book be in
order to maximize the bookstore's total profits on the book?


\item (2pts) You need to make a box (with no lid) out of a piece of cardboard 
that is 10cm by 20cm.  What is the maximum volume of the box?

\end{enumerate}





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