(*********************************************************************** 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). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. 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[ 27041, 923]*) (*NotebookOutlinePosition[ 29059, 989]*) (* CellTagsIndexPosition[ 28741, 975]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["\<\ A Method for Finding the Maxima, Minima and Inflection Points of a \ Function\ \>", "Subtitle", TextAlignment->Center, FontColor->RGBColor[1, 0, 0], Background->GrayLevel[0.900008]], Cell[TextData[{ "This notebook gives the user a simple method of determining the maxima, \ minima and points of inflection of a function, using ", StyleBox["Mathematica", FontSlant->"Italic"], ". First of all, it teaches you ", ButtonBox["how to define a function", ButtonData:>"enterfunction", ButtonStyle->"Hyperlink"], " and ", ButtonBox["graph", ButtonData:>"graph", ButtonStyle->"Hyperlink"], " it in ", StyleBox["Mathematica", FontSlant->"Italic"], " and then how to use the graph to find the turning points (extrema) of the \ function. Second of all, this tutorial teaches you how to use the first and \ second derivative of the function to find the extrema or points of inflection \ of a function. You will also find ", ButtonBox["sample problems", ButtonData:>"examples", ButtonStyle->"Hyperlink"], " at the bottom of this tutorial notebook, with or without using ", StyleBox["Mathematica", FontSlant->"Italic"], ".", StyleBox[ " All the blue text in this notebook is linked to another notebook or \ another section in the notebook.", FontColor->RGBColor[1, 0, 0]] }], "Text", TextAlignment->Left, CellTags->"top"], Cell[CellGroupData[{ Cell[TextData[{ "Enter the function you wish to examine in ", StyleBox["Mathematica", FontSlant->"Italic"], " , giving it a name (for example, the function y) and plot it." }], "Section", FontSize->18, CellTags->"enterfunction"], Cell[TextData[{ "To define a function in ", StyleBox["Mathematica", FontSlant->"Italic"], " , you have to enter it as shown below. The \"=\" sign is used to assign \ a value to any variable that you select such as x or y. Here, I have \ assigned an equation in x to the variable y." }], "Text", TextAlignment->Left, FontSlant->"Italic", Background->GrayLevel[0.900008]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\ y\ = \ 2\ x\^3 - 3\ x\^2 - 12\ x + 5\ \ \ \)\)], "Input"], Cell[BoxData[ \(5 - 12\ x - 3\ x\^2 + 2\ x\^3\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " always outputs functions in this way. Polynomials are displayed with the \ constant term coming first, followed by the term in x, the term in ", Cell[BoxData[ \(x\^2\)]], " and so on." }], "Text", FontSlant->"Italic", Background->GrayLevel[0.900008]], Cell["\<\ \tA plot of this function can now be obtained with the following \ Mathematica command line.\ \>", "Text"], Cell[BoxData[ \(Plot[y, {x, \(-3\), 3}, \ AxesLabel -> {"\", \ "\<\>"}, \ PlotLabel -> \ "\"] \)], "Input", CellTags->"range"], Cell[TextData[{ "To understand the ", StyleBox["Mathematica", FontSlant->"Italic"], " \"Plot\" command and the parameters used in ", StyleBox["Mathematica", FontSlant->"Italic"], ", click ", ButtonBox["here.", ButtonData:>{ URL[ "http://mathforum.org/spimsow/notebooks/Plot.nb"], None}, ButtonStyle->"Hyperlink"], " " }], "Text", FontSlant->"Italic", Background->GrayLevel[0.900008], CellTags->"plotlinkback"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix 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