(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 26616, 995]*) (*NotebookOutlinePosition[ 27670, 1031]*) (* CellTagsIndexPosition[ 27626, 1027]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData[ "Mathematics 161 Laboratory 5 \ October 1, 1992\n\t \nName: _____________________________ Lab \ Partner: ___________________________\n\t \nConsulted with: \ ____________________________________________________________"], "Text", CellMargins->{{17, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{1, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData["\[Copyright] Lafayette College, 1994"], "SmallText", Evaluatable->False, TextAlignment->Right, AspectRatioFixed->True], Cell[TextData["\t Properties of Derivatives"], "Title", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ StyleBox["\tIn this laboratory you will use ", Evaluatable->False, AspectRatioFixed->True], StyleBox["Mathematica", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[ "'s symbolic differentiation and graphing facilities to begin exploring \ some properties of derivatives.", Evaluatable->False, AspectRatioFixed->True] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData["Part 0: Differentiation by Rules"], "Section", Evaluatable->False, AspectRatioFixed->True], Cell[TextData["Preliminaries"], "Subsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "As in last week's lab, we will use some special commands contained in the \ \"DerivativeGraphics\" package; recall, we input the package as follows:"], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData["<True], Cell[TextData[{ StyleBox["Syntax for Differentiation in ", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Plain"], StyleBox["Mathematica", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Plain", FontSlant->"Italic"] }], "Subsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ StyleBox[ "Let's define a function to differentiate. 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Define it in ", Evaluatable->False, AspectRatioFixed->True], StyleBox["Mathematica", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" now.", Evaluatable->False, AspectRatioFixed->True] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ StyleBox["(a) The command ", Evaluatable->False, AspectRatioFixed->True], StyleBox["SecantLine[h, 0, 5, {x, -1/2, 6}]", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Courier", FontWeight->"Bold"], StyleBox[" will generate a plot of the graph of ", Evaluatable->False, AspectRatioFixed->True], StyleBox["h", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" and the secant line for the graph passing through (0, ", Evaluatable->False, AspectRatioFixed->True], StyleBox["h", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox["(0)) and (5, ", Evaluatable->False, AspectRatioFixed->True], StyleBox["h", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox["(5)). Assign this plot the name ", Evaluatable->False, AspectRatioFixed->True], StyleBox["plot1", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Courier", FontWeight->"Bold"], StyleBox[" by entering ", Evaluatable->False, AspectRatioFixed->True], StyleBox["plot1 = %", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Courier", FontWeight->"Bold"], StyleBox[". (", Evaluatable->False, AspectRatioFixed->True], StyleBox["Mathematica", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" will respond with ", Evaluatable->False, AspectRatioFixed->True], StyleBox["-Graphics-", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Courier"], StyleBox[ ", indicating it has assigned a graphic image as the \"value\" of ", Evaluatable->False, AspectRatioFixed->True], StyleBox["plot1", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Courier", FontWeight->"Bold"], StyleBox[".)", Evaluatable->False, AspectRatioFixed->True] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "(b)\tUse Mathematica to determine the exact slope of the secant line in this \ plot. (Do not try to read coordinates off the plot; use the two points on the \ line whose coordinates you know.) 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(You must substitute the value for ", Evaluatable->False, AspectRatioFixed->True], StyleBox["c", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[ " you have found in order for the command to work.) Assign this plot the \ name ", Evaluatable->False, AspectRatioFixed->True], StyleBox["plot2", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Courier", FontWeight->"Bold"], StyleBox[ ". To see the secant line and the tangent line on the same plot, enter ", Evaluatable->False, AspectRatioFixed->True], StyleBox["Show[plot1, plot2]", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Courier", FontWeight->"Bold"], StyleBox[ ". Print out this plot and, based on the plot, answer the following \ question: do the two lines have the same slope? 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