%Derivatives %If you modify this file, please indicate here and in the footnote %Math263A \documentclass[12pt]{article} \usepackage{times} \pagestyle{empty} \addtolength{\textwidth}{1.2in} \addtolength{\textheight}{1.2in} \addtolength{\oddsidemargin}{-.58in} \addtolength{\evensidemargin}{-.58in} \renewcommand{\baselinestretch}{1.0} \parindent = 0cm \parskip = .1cm \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.} \end{document}