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\begin{document}


\title{On-line Math 21}


\email{david.johnson@lehigh.edu}


\urladdr{http://www.lehigh.edu/\textasciitilde{}dlj0}

\maketitle

\subsection{The Mean Value Theorem}

\begin{example}
My commute to work involves a stretch of the Northeast Extension of the Pennsylvania
Turnpike. I get on (at Plymouth Meeting), mile marker 20, and am handed a ticket,
with the time stamped on it. When I get off, at the Quakertown exit, mile 44,
21 minutes later, the ticket taker hands me my change and a speeding citation.
Have I been wronged?
\end{example}

\subsubsection*{Solution}

Since the elapsed time of my travel between getting on, and getting off, the
turnpike was only 21 minutes, and yet I travelled 24 miles, according to the
MVT at some time \( t=c \) my speed \( v(c) \) along the road was \[
v(c)=\frac{44-20}{21-0}=68.57mph.\]
No, since the speed limit is never more than 65 mph I was speeding and deserved
the ticket. I wouldn't have much sympathy in court, either, since half of that
portion of the road has a 55 mph speed limit. 

Don't think that this sort of automatic ticketing can't happen. 
\end{document}
