%Derivatives
%If you modify this file, please indicate here and in the footnote
%Math263A

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\begin{document}

\begin{center}
{\Large
Derivatives\footnote{
Copyright \copyright 2002 Larry Snyder and Todd Young.  All rights reserved.
Please address comments to young@math.ohiou.edu.}}
\end{center}

\begin{enumerate}
\item Try the following commands:
    \begin{enumerate}
      \item  \verb&syms x &
      \item  \verb&f = x^2 &
      \item  \verb&f1 = diff(f) &
      \item  \verb&X = -3:.05:3; & \dotfill Makes \verb&X& into an array with entries 
		from \verb$-3$ to \verb$3$
      \item  \verb&F = subs(f, X); & 
      \item  \verb&F1 = subs(f1, X); &
      \item  \verb&plot(X, F, 'b', X, F1, 'r') &
      \item Explain exactly what happened.
   \end{enumerate}

\item\label{rat} Repeat the above procedure for the function
$$
	g(x) = \frac{x^5 + x^3 + 2}{8x + 1}
    \qquad 
    \verb&(Input as: g = (x^5 + x^3 + 2) / (8*x + 1))&.
\]

\item Use the command  \verb& ezplot(g1, [0 3]) & and then
 change the interval until you can accurately guess a solution of $g'(x) = 0$.
  Then try:
    \begin{enumerate}
      \item  Enter \verb& solve(g1) & and describe the results. Which part of the output
             is relevant? Did the computer find this output symbolically or numerically?
      \item  What is the percentage error of your guess.
    \end{enumerate}

\item Prepare a brief (\verb$< $1 page) written report answering all
      the questions. Use complete sentences and standard mathematical notation. 
      Do {\bf not} get a printout.

\end{enumerate}

\vfill
\noindent
\textsf{The user must consider the derivative as a function, and they must
consider issues of scale in plotting functions with asymptotes.}

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