\hfill \hfill } %} \newtheorem{theorem}{Theorem} \newtheorem{acknowledgement}[theorem]{Acknowledgement} \newtheorem{algorithm}[theorem]{Algorithm} \newtheorem{axiom}[theorem]{Axiom} \newtheorem{case}[theorem]{Case} \newtheorem{claim}[theorem]{Claim} \newtheorem{conclusion}[theorem]{Conclusion} \newtheorem{condition}[theorem]{Condition} \newtheorem{conjecture}[theorem]{Conjecture} \newtheorem{corollary}[theorem]{Corollary} \newtheorem{criterion}[theorem]{Criterion} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{exercise}[theorem]{Exercise} \newtheorem{lemma}[theorem]{Lemma} \newtheorem{notation}[theorem]{Notation} \newtheorem{problem}[theorem]{Problem} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{remark}[theorem]{Remark} \newtheorem{solution}[theorem]{Solution} \newtheorem{summary}[theorem]{Summary} \newenvironment{proof}[1][Proof]{\noindent\textbf{#1.} }{\ \rule{0.5em}{0.5em}} \input{tcilatex} \geometry{left=0.4in,right=0.5in,top=0.5in,bottom=0.4in} \pagestyle{fancy} \lhead{\color{blue} \Large Lecture Notes} \lfoot{\small \copyright $\;$ copyright Hidegkuti, Powell, 2012} \rfoot{\small Last revised: April 10, 2012} \cfoot{} \chead{\LARGE Graphing the Antiderivative} \rhead{\large page \thepage} \textwidth 7.5in \textheight 9.5in \setlength{\headheight}{28pt} \setlength{\parindent}{0pt} \begin{document} The picture below shows the graph of $f^{\prime }$, the derivative a function $f$. \ Sketch the graph of $f$ in the same coordinate system.\bigskip \qquad 1.) \ \FRAME{dtbpFX}{5.0194in}{3.0113in}{0pt}{}{}{Plot}{\special{language "Scientific Word";type "MAPLEPLOT";width 5.0194in;height 3.0113in;depth 0pt;display "USEDEF";plot_snapshots TRUE;mustRecompute FALSE;lastEngine "MuPAD";xmin "-5.01";xmax "5.01";xviewmin "-5.01";xviewmax "5.01";yviewmin "-70";yviewmax "80";viewset"XY";rangeset"X";plottype 4;plotticks 1;num-x-ticks 11;numpoints 100;plotstyle "patch";axesstyle "normal";xis \TEXUX{x};yis \TEXUX{y};var1name \TEXUX{$x$};var2name \TEXUX{$y$};function \TEXUX{$\left( x+3\right) x\left( x-3\right) ^{2}$};linecolor "black";linestyle 1;pointstyle "point";linethickness 3;lineAttributes "Solid";var1range "-5.01,5.01";num-x-gridlines 100;curveColor "[flat::RGB:0000000000]";curveStyle "Line";valid_file "T";tempfilename 'MY8MN70S.wmf';tempfile-properties "XPR";}} \bigskip \bigskip \qquad 2.) \ \FRAME{dtbpFX}{5.0194in}{3.0113in}{0pt}{}{}{Plot}{\special{language "Scientific Word";type "MAPLEPLOT";width 5.0194in;height 3.0113in;depth 0pt;display "USEDEF";plot_snapshots TRUE;mustRecompute FALSE;lastEngine "MuPAD";xmin "-3.01";xmax "5.01";xviewmin "-3.01";xviewmax "5.01";yviewmin "-50";yviewmax "60";viewset"XY";rangeset"X";plottype 4;plotticks 1;num-x-ticks 9;numpoints 100;plotstyle "patch";axesstyle "normal";xis \TEXUX{x};yis \TEXUX{y};var1name \TEXUX{$x$};var2name \TEXUX{$y$};function \TEXUX{$\left( x-4\right) \left( x-2\right) ^{2}x\left( x+2\right) $};linecolor "black";linestyle 1;pointstyle "point";linethickness 3;lineAttributes "Solid";var1range "-3.01,5.01";num-x-gridlines 100;curveColor "[flat::RGB:0000000000]";curveStyle "Line";valid_file "T";tempfilename 'MY8MOG0T.wmf';tempfile-properties "XPR";}}\pagebreak \bigskip \qquad 3.) \ \FRAME{dtbpFX}{5.0194in}{3.0113in}{0pt}{}{}{Plot}{\special{language "Scientific Word";type "MAPLEPLOT";width 5.0194in;height 3.0113in;depth 0pt;display "USEDEF";plot_snapshots TRUE;mustRecompute FALSE;lastEngine "MuPAD";xmin "-4.01";xmax "4.01";xviewmin "-4.01";xviewmax "4.01";yviewmin "-80";yviewmax "80";viewset"XY";rangeset"X";plottype 4;plotticks 1;num-x-ticks 9;numpoints 100;plotstyle "patch";axesstyle "normal";xis \TEXUX{x};yis \TEXUX{y};var1name \TEXUX{$x$};var2name \TEXUX{$y$};function \TEXUX{$3\left( -1\right) \left( x+2\right) \left( x+1\right) ^{2}\left( x-1\right) \left( x-2\right) ^{2}\left( x-3\right) $};linecolor "black";linestyle 1;pointstyle "point";linethickness 3;lineAttributes "Solid";var1range "-4.01,4.01";num-x-gridlines 100;curveColor "[flat::RGB:0000000000]";curveStyle "Line";valid_file "T";tempfilename 'MY8MOG0U.wmf';tempfile-properties "XPR";}} \bigskip \bigskip \bigskip \qquad 4.) \ \FRAME{dtbpFX}{5.0194in}{3.0113in}{0pt}{}{}{Plot}{\special{language "Scientific Word";type "MAPLEPLOT";width 5.0194in;height 3.0113in;depth 0pt;display "USEDEF";plot_snapshots TRUE;mustRecompute FALSE;lastEngine "MuPAD";xmin "-5.01";xmax "5.01";xviewmin "-5.01";xviewmax "5.01";yviewmin "-70";yviewmax "85";viewset"XY";rangeset"X";plottype 4;plotticks 1;num-x-ticks 11;numpoints 100;plotstyle "patch";axesstyle "normal";xis \TEXUX{x};yis \TEXUX{y};var1name \TEXUX{$x$};var2name \TEXUX{$y$};function \TEXUX{$\dfrac{1}{10}\left( x+3\right) \left( x+2\right) ^{2}x\left( x-1\right) \left( x-3\right) \left( x-4\right) ^{2}$};linecolor "black";linestyle 1;pointstyle "point";linethickness 3;lineAttributes "Solid";var1range "-5.01,5.01";num-x-gridlines 100;curveColor "[flat::RGB:0000000000]";curveStyle "Line";valid_file "T";tempfilename 'MY8MOG0V.wmf';tempfile-properties "XPR";}} \pagebreak \begin{center} {\Large Answers\bigskip } \end{center} \qquad 1.) \ \FRAME{dtbpFX}{5.0194in}{3.0113in}{0pt}{}{}{Plot}{\special{language "Scientific Word";type "MAPLEPLOT";width 5.0194in;height 3.0113in;depth 0pt;display "USEDEF";plot_snapshots TRUE;mustRecompute FALSE;lastEngine "MuPAD";xmin "-5.01";xmax "5.01";xviewmin "-5.01";xviewmax "5.01";yviewmin "-70";yviewmax "80";viewset"XY";rangeset"X";plottype 4;plotticks 1;num-x-ticks 11;numpoints 100;plotstyle "patch";axesstyle "normal";xis \TEXUX{x};yis \TEXUX{y};var1name \TEXUX{$x$};var2name \TEXUX{$y$};function \TEXUX{$\left( x+3\right) x\left( x-3\right) ^{2}$};linecolor "black";linestyle 1;pointstyle "point";linethickness 3;lineAttributes "Solid";var1range "-5.01,5.01";num-x-gridlines 100;curveColor "[flat::RGB:0000000000]";curveStyle "Line";function \TEXUX{$-20+\left( \dfrac{27}{2}x^{2}-3x^{3}-\dfrac{3}{4}x^{4}+\dfrac{1}{5}x^{5}\right) $};linecolor "blue";linestyle 1;pointstyle "point";linethickness 3;lineAttributes "Solid";var1range "-5.01,5.01";num-x-gridlines 100;curveColor "[flat::RGB:0x00000080]";curveStyle "Line";valid_file "T";tempfilename 'MY8MQ70Z.wmf';tempfile-properties "XPR";}} \bigskip \bigskip \qquad 2.) \ \FRAME{dtbpFX}{5.0194in}{3.0113in}{0pt}{}{}{Plot}{\special{language "Scientific Word";type "MAPLEPLOT";width 5.0194in;height 3.0113in;depth 0pt;display "USEDEF";plot_snapshots TRUE;mustRecompute FALSE;lastEngine "MuPAD";xmin "-3.01";xmax "5.01";xviewmin "-3.01";xviewmax "5.01";yviewmin "-50";yviewmax "60";viewset"XY";rangeset"X";plottype 4;plotticks 1;num-x-ticks 9;numpoints 100;plotstyle "patch";axesstyle "normal";xis \TEXUX{x};yis \TEXUX{y};var1name \TEXUX{$x$};var2name \TEXUX{$y$};function \TEXUX{$\left( x-4\right) \left( x-2\right) ^{2}x\left( x+2\right) $};linecolor "black";linestyle 1;pointstyle "point";linethickness 3;lineAttributes "Solid";var1range "-3.01,5.01";num-x-gridlines 100;curveColor "[flat::RGB:0000000000]";curveStyle "Line";function \TEXUX{$23+\left( 8x^{3}-16x^{2}+x^{4}-\dfrac{6}{5}x^{5}+\dfrac{1}{6}x^{6}\right) $};linecolor "blue";linestyle 1;pointstyle "point";linethickness 3;lineAttributes "Solid";var1range "-3.01,5.01";num-x-gridlines 100;curveColor "[flat::RGB:0x00000080]";curveStyle "Line";valid_file "T";tempfilename 'MY8MQ40Y.wmf';tempfile-properties "XPR";}}\pagebreak \bigskip \qquad 3.) \ \FRAME{dtbpFX}{5.0194in}{3.0113in}{0pt}{}{}{Plot}{\special{language "Scientific Word";type "MAPLEPLOT";width 5.0194in;height 3.0113in;depth 0pt;display "USEDEF";plot_snapshots TRUE;mustRecompute FALSE;lastEngine "MuPAD";xmin "-4.01";xmax "4.01";xviewmin "-4.01";xviewmax "4.01";yviewmin "-80";yviewmax "80";viewset"XY";rangeset"X";plottype 4;plotticks 1;num-x-ticks 9;numpoints 100;plotstyle "patch";axesstyle "normal";xis \TEXUX{x};yis \TEXUX{y};var1name \TEXUX{$x$};var2name \TEXUX{$y$};function \TEXUX{$3\left( -1\right) \left( x+2\right) \left( x+1\right) ^{2}\left( x-1\right) \left( x-2\right) ^{2}\left( x-3\right) $};linecolor "black";linestyle 1;pointstyle "point";linethickness 3;lineAttributes "Solid";var1range "-4.01,4.01";num-x-gridlines 100;curveColor "[flat::RGB:0000000000]";curveStyle "Line";function \TEXUX{$-20+\left( 46x^{3}-6x^{2}-72x+\dfrac{3}{4}x^{4}-\dfrac{78}{5}x^{5}+2x^{6}+% \dfrac{12}{7}x^{7}-\allowbreak \dfrac{3}{8}x^{8}\right) $};linecolor "blue";linestyle 1;pointstyle "point";linethickness 3;lineAttributes "Solid";var1range "-4.01,4.01";num-x-gridlines 100;curveColor "[flat::RGB:0x00000080]";curveStyle "Line";valid_file "T";tempfilename 'MY8MOG0W.wmf';tempfile-properties "XPR";}} \bigskip \bigskip \bigskip \qquad 4.) \ \FRAME{dtbpFX}{5.0194in}{3.0113in}{0pt}{}{}{Plot}{\special{language "Scientific Word";type "MAPLEPLOT";width 5.0194in;height 3.0113in;depth 0pt;display "USEDEF";plot_snapshots TRUE;mustRecompute FALSE;lastEngine "MuPAD";xmin "-5.01";xmax "5.01";xviewmin "-5.01";xviewmax "5.01";yviewmin "-70";yviewmax "85";viewset"XY";rangeset"X";plottype 4;plotticks 1;num-x-ticks 11;numpoints 100;plotstyle "patch";axesstyle "normal";xis \TEXUX{x};yis \TEXUX{y};var1name \TEXUX{$x$};var2name \TEXUX{$y$};function \TEXUX{$\dfrac{1}{10}\left( x+3\right) \left( x+2\right) ^{2}x\left( x-1\right) \left( x-3\right) \left( x-4\right) ^{2}$};linecolor "black";linestyle 1;pointstyle "point";linethickness 3;lineAttributes "Solid";var1range "-5.01,5.01";num-x-gridlines 100;curveColor "[flat::RGB:0000000000]";curveStyle "Line";function \TEXUX{$15+\left( \dfrac{144}{5}x^{2}-\dfrac{48}{5}x^{3}-\dfrac{23}{2}x^{4}+% \dfrac{52}{25}x^{5}+\dfrac{89}{60}x^{6}-\dfrac{17}{70}x^{7}-\allowbreak \dfrac{1}{16}x^{8}+\dfrac{1}{90}x^{9}\right) $};linecolor "blue";linestyle 1;pointstyle "point";linethickness 3;lineAttributes "Solid";var1range "-5.01,5.01";num-x-gridlines 100;curveColor "[flat::RGB:0x00000080]";curveStyle "Line";valid_file "T";tempfilename 'MY8MOG0X.wmf';tempfile-properties "XPR";}} \bigskip \vspace{1.3in}{\small %TCIMACRO{\TeXButton{\small}{\small}}% %BeginExpansion \small% %EndExpansion } \href{https://teaching.martahidegkuti.com/shared/lnotes/lecturenotes.html}{% For more documents like this, visit our page at\ https://teaching.martahidegkuti.com and click on Lecture Notes. \ E-mail questions or comments to mhidegkuti@ccc.edu.} \end{document}