(* Content-type: application/vnd.wolfram.cdf.text *) (*** Wolfram CDF File ***) (* http://www.wolfram.com/cdf *) (* CreatedBy='Mathematica 9.0' *) (*************************************************************************) (* *) (* The Mathematica License under which this file was created prohibits *) (* restricting third parties in receipt of this file from republishing *) (* or redistributing it by any means, including but not limited to *) (* rights management or terms of use, without the express consent of *) (* Wolfram Research, Inc. For additional information concerning CDF *) (* licensing and redistribution see: *) (* *) (* www.wolfram.com/cdf/adopting-cdf/licensing-options.html *) (* *) (*************************************************************************) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 1063, 20] NotebookDataLength[ 80905, 1655] NotebookOptionsPosition[ 81299, 1646] NotebookOutlinePosition[ 81908, 1670] CellTagsIndexPosition[ 81865, 1667] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ RowBox[{Cell[TextData[{ StyleBox["\t", FontFamily->"Optima", FontSize->18, FontWeight->"Plain", Background->RGBColor[1, 0.85, 0.85]], StyleBox[" F-Tool : ", FontFamily->"Optima", FontSize->18, FontWeight->"Plain", Background->None], StyleBox["F-Cosine", FontFamily->"Optima", FontSize->18, Background->None], StyleBox["\n\tAuthors : ", FontFamily->"Optima", FontSize->18, FontWeight->"Plain", Background->None], StyleBox["Ana C. 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\[Element] \[DoubleStruckCapitalZ] "}]}]], 16]]]]], Manipulate`Dump`ThisIsNotAControl}, { Hold[ Style[ " \!\(\*\nStyleBox[\"Inflection\",\nFontSize->14]\)\!\(\*\nStyleBox[\ \" \",\nFontSize->14]\)\!\(\*\nStyleBox[\"Points\",\nFontSize->14]\)", Bold]], Manipulate`Dump`ThisIsNotAControl}, { Hold[""], Manipulate`Dump`ThisIsNotAControl}, { Hold[ Dynamic[ If[$CellContext`a$$ $CellContext`b$$ == 0, $CellContext`TradForm[ Row[{" No Inflection Points"}], 16], If[$CellContext`c$$ - Pi/2 != 0, $CellContext`TradForm[ If[$CellContext`rationalize$$, Row[{" \!\(\*\nStyleBox[\"y\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\n\ FontSlant->\"Italic\"]\)=\!\(\*\nStyleBox[\" \",\nFontSize->9]\)", Rationalize[$CellContext`d$$], " for all \!\(\*\nStyleBox[\"x\",\nFontSlant->\"Italic\"]\) \ = ", Rationalize[$CellContext`c$$] - Pi/2, If[$CellContext`b$$ > 0, " + ", " "], If[$CellContext`b$$ == -1, "-", If[$CellContext`b$$ != 1, Rationalize[1/(2 $CellContext`b$$)]]], "\!\(\*\nStyleBox[\" \",\nFontSize->9]\)\!\(\*\n\ StyleBox[\"k\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\n\ FontSize->9,\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"\[Pi]\",\n\ FontSlant->\"Italic\"]\), \!\(\*\nStyleBox[\"k\",\n\ FontSlant->\"Italic\"]\) \[Element] \[DoubleStruckCapitalZ] "}], Row[{" \!\(\*\nStyleBox[\"y\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)\ \[TildeEqual]\!\(\*\nStyleBox[\" \",\nFontSize->9]\)", $CellContext`d$$, " for all \!\(\*\nStyleBox[\"x\",\nFontSlant->\"Italic\"]\) \ \[TildeEqual] ", $CellContext`c$$ - Pi/2, If[$CellContext`b$$ > 0, " + ", " "], If[$CellContext`b$$ == -1, "-", If[$CellContext`b$$ != 1, 1/(2 $CellContext`b$$)]], "\!\(\*\nStyleBox[\" \",\nFontSize->9]\)\!\(\*\n\ StyleBox[\"k\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\n\ FontSize->9,\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"\[Pi]\",\n\ FontSlant->\"Italic\"]\), \!\(\*\nStyleBox[\"k\",\n\ FontSlant->\"Italic\"]\) \[Element] \[DoubleStruckCapitalZ] "}]], 16], $CellContext`TradForm[ If[$CellContext`rationalize$$, Row[{" \!\(\*\nStyleBox[\"y\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\n\ FontSlant->\"Italic\"]\)=\!\(\*\nStyleBox[\" \",\nFontSize->9]\)", Rationalize[$CellContext`d$$], " for all \!\(\*\nStyleBox[\"x\",\nFontSlant->\"Italic\"]\) \ = ", If[$CellContext`b$$ == -1, "-", If[$CellContext`b$$ != 1, Rationalize[1/(2 $CellContext`b$$)]]], "\!\(\*\nStyleBox[\" \",\nFontSize->9]\)\!\(\*\n\ StyleBox[\"k\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\n\ FontSize->9,\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"\[Pi]\",\n\ FontSlant->\"Italic\"]\), \!\(\*\nStyleBox[\"k\",\n\ FontSlant->\"Italic\"]\) \[Element] \[DoubleStruckCapitalZ] "}], Row[{" \!\(\*\nStyleBox[\"y\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)\ \[TildeEqual]\!\(\*\nStyleBox[\" \",\nFontSize->9]\)", $CellContext`d$$, " for all \!\(\*\nStyleBox[\"x\",\nFontSlant->\"Italic\"]\) \ \[TildeEqual] ", If[$CellContext`b$$ == -1, "-", If[$CellContext`b$$ != 1, 1/(2 $CellContext`b$$)]], "\!\(\*\nStyleBox[\" \",\nFontSize->9]\)\!\(\*\n\ StyleBox[\"k\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\n\ FontSize->9,\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"\[Pi]\",\n\ FontSlant->\"Italic\"]\), \!\(\*\nStyleBox[\"k\",\n\ FontSlant->\"Italic\"]\) \[Element] \[DoubleStruckCapitalZ] "}]], 16]]]]], Manipulate`Dump`ThisIsNotAControl}, { Hold[ Style[ " \!\(\*\nStyleBox[\"Analytic\",\nFontSize->14]\)\!\(\*\nStyleBox[\" \ \",\nFontSize->14]\)\!\(\*\nStyleBox[\"Expressions\",\nFontSize->14]\)", Bold]], Manipulate`Dump`ThisIsNotAControl}, { Hold[""], Manipulate`Dump`ThisIsNotAControl}, { Hold[ Dynamic[ $CellContext`TradForm[ Row[{" \!\(\*\nStyleBox[\"f\",\nFontSlant->\"Italic\"]\)\!\(\*\n\ StyleBox[\"(\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"x\",\nFontSlant->\ \"Italic\"]\))", If[$CellContext`rationalize$$, " = ", " \[TildeEqual] "], If[$CellContext`rationalize$$, $CellContext`Rf[$CellContext`x, $CellContext`a$$, \ $CellContext`b$$, $CellContext`c$$, $CellContext`d$$], $CellContext`f[$CellContext`x, $CellContext`a$$, \ $CellContext`b$$, $CellContext`c$$, $CellContext`d$$]]}], 16]]], Manipulate`Dump`ThisIsNotAControl}, { Hold[""], Manipulate`Dump`ThisIsNotAControl}, { Hold[""], Manipulate`Dump`ThisIsNotAControl}, { Hold[ Dynamic[ $CellContext`TradForm[ If[$CellContext`firstD$$, Row[{" \!\(\*\nStyleBox[\"f\.b4\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"(\",\nFontSlant->\"Italic\"]\)\!\(\ \*\nStyleBox[\"x\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\")\",\n\ FontSlant->\"Italic\"]\)", If[$CellContext`rationalize$$, " = ", " \[TildeEqual] "], If[$CellContext`rationalize$$, $CellContext`RDf[$CellContext`x, $CellContext`a$$, \ $CellContext`b$$, $CellContext`c$$, $CellContext`d$$], $CellContext`Df[$CellContext`x, $CellContext`a$$, \ $CellContext`b$$, $CellContext`c$$, $CellContext`d$$]]}], Row[{" \!\(\*\nStyleBox[\"f\.b4\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"(\",\nFontSlant->\"Italic\"]\)\!\(\ \*\nStyleBox[\"x\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\")\",\n\ FontSlant->\"Italic\"]\)"}]], 16]]], Manipulate`Dump`ThisIsNotAControl}, { Hold[""], Manipulate`Dump`ThisIsNotAControl}, { Hold[""], Manipulate`Dump`ThisIsNotAControl}, { Hold[ Dynamic[ $CellContext`TradForm[ If[$CellContext`secondD$$, Row[{" \!\(\*\nStyleBox[\"f\.b4\.b4\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"(\",\nFontSlant->\"Italic\"]\)\!\(\ \*\nStyleBox[\"x\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\")\",\n\ FontSlant->\"Italic\"]\)", If[$CellContext`rationalize$$, " = ", " \[TildeEqual] "], If[$CellContext`rationalize$$, $CellContext`RDDf[$CellContext`x, $CellContext`a$$, \ $CellContext`b$$, $CellContext`c$$, $CellContext`d$$], $CellContext`DDf[$CellContext`x, $CellContext`a$$, \ $CellContext`b$$, $CellContext`c$$, $CellContext`d$$]]}], Row[{" \!\(\*\nStyleBox[\"f\.b4\.b4\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"(\",\nFontSlant->\"Italic\"]\)\!\(\ \*\nStyleBox[\"x\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\")\",\n\ FontSlant->\"Italic\"]\)"}]], 16]]], Manipulate`Dump`ThisIsNotAControl}, { Hold[""], Manipulate`Dump`ThisIsNotAControl}, { Hold[""], Manipulate`Dump`ThisIsNotAControl}, { Hold[ Dynamic[ $CellContext`TradForm[ If[$CellContext`xx$$, Row[{" \!\(\*\nStyleBox[\"-\",\nFontSlant->\"Italic\"]\)\!\(\*\n\ StyleBox[\"f\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"(\",\nFontSlant->\ \"Italic\"]\)\!\(\*\nStyleBox[\"x\",\nFontSlant->\"Italic\"]\)\!\(\*\n\ StyleBox[\")\",\nFontSlant->\"Italic\"]\)", If[$CellContext`rationalize$$, " = ", " \[TildeEqual] "], If[$CellContext`rationalize$$, -$CellContext`Rf[$CellContext`x, \ $CellContext`a$$, $CellContext`b$$, $CellContext`c$$, $CellContext`d$$], \ -$CellContext`f[$CellContext`x, $CellContext`a$$, $CellContext`b$$, \ $CellContext`c$$, $CellContext`d$$]]}], Row[{" \!\(\*\nStyleBox[\"-\",\nFontSlant->\"Italic\"]\)\!\(\*\n\ StyleBox[\"f\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"(\",\nFontSlant->\ \"Italic\"]\)\!\(\*\nStyleBox[\"x\",\nFontSlant->\"Italic\"]\)\!\(\*\n\ StyleBox[\")\",\nFontSlant->\"Italic\"]\)"}]], 16]]], Manipulate`Dump`ThisIsNotAControl}, { Hold[""], Manipulate`Dump`ThisIsNotAControl}, { Hold[""], Manipulate`Dump`ThisIsNotAControl}, { Hold[ Dynamic[ $CellContext`TradForm[ If[$CellContext`yy$$, Row[{" \!\(\*\nStyleBox[\"f\",\nFontSlant->\"Italic\"]\)\!\(\*\n\ StyleBox[\"(\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"-\",\nFontSlant->\ \"Italic\"]\)\!\(\*\nStyleBox[\"x\",\nFontSlant->\"Italic\"]\)\!\(\*\n\ StyleBox[\")\",\nFontSlant->\"Italic\"]\)", $CellContext`f[-$CellContext`x], If[$CellContext`rationalize$$, " = ", " \[TildeEqual] "], If[$CellContext`rationalize$$, $CellContext`Rf[-$CellContext`x, $CellContext`a$$, \ $CellContext`b$$, $CellContext`c$$, $CellContext`d$$], $CellContext`f[-$CellContext`x, $CellContext`a$$, \ $CellContext`b$$, $CellContext`c$$, $CellContext`d$$]]}], Row[{" \!\(\*\nStyleBox[\"f\",\nFontSlant->\"Italic\"]\)\!\(\*\n\ StyleBox[\"(\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"-\",\nFontSlant->\ \"Italic\"]\)\!\(\*\nStyleBox[\"x\",\nFontSlant->\"Italic\"]\)\!\(\*\n\ StyleBox[\")\",\nFontSlant->\"Italic\"]\)"}]], 16]]], Manipulate`Dump`ThisIsNotAControl}, { Hold[""], Manipulate`Dump`ThisIsNotAControl}, { Hold[""], Manipulate`Dump`ThisIsNotAControl}, { Hold[ Dynamic[ $CellContext`TradForm[ If[$CellContext`origin$$, Row[{" \!\(\*\nStyleBox[\"-\",\nFontSlant->\"Italic\"]\)\!\(\*\n\ StyleBox[\"f\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"(\",\nFontSlant->\ \"Italic\"]\)\!\(\*\nStyleBox[\"-\",\nFontSlant->\"Italic\"]\)\!\(\*\n\ StyleBox[\"x\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\")\",\nFontSlant->\ \"Italic\"]\)", If[$CellContext`rationalize$$, " = ", " \[TildeEqual] "], If[$CellContext`rationalize$$, -$CellContext`Rf[-$CellContext`x, \ $CellContext`a$$, $CellContext`b$$, $CellContext`c$$, $CellContext`d$$], \ -$CellContext`f[-$CellContext`x, $CellContext`a$$, $CellContext`b$$, \ $CellContext`c$$, $CellContext`d$$]]}], Row[{" \!\(\*\nStyleBox[\"-\",\nFontSlant->\"Italic\"]\)\!\(\*\n\ StyleBox[\"f\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"(\",\nFontSlant->\ \"Italic\"]\)\!\(\*\nStyleBox[\"-\",\nFontSlant->\"Italic\"]\)\!\(\*\n\ StyleBox[\"x\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\")\",\nFontSlant->\ \"Italic\"]\)"}]], 16]]], Manipulate`Dump`ThisIsNotAControl}, { Hold[ Style[ " \!\(\*\nStyleBox[\"Tangent\",\nFontSize->14]\)\!\(\*\nStyleBox[\" \ \",\nFontSize->14]\)\!\(\*\nStyleBox[\"Line\",\nFontSize->14]\)\!\(\*\n\ StyleBox[\" \",\nFontSize->14]\)\!\(\*\nStyleBox[\"Equation\",\nFontSize->14]\ \)", Bold]], Manipulate`Dump`ThisIsNotAControl}, { Hold[""], Manipulate`Dump`ThisIsNotAControl}, { Hold[ Dynamic[ $CellContext`TradForm[ Row[{" \!\(\*\nStyleBox[\"y\",\nFontSlant->\"Italic\"]\)", If[$CellContext`rationalize$$, " = ", " \[TildeEqual] "], If[$CellContext`tangent$$, If[$CellContext`rationalize$$, $CellContext`TanEqR[$CellContext`x0$$, $CellContext`a$$, \ $CellContext`b$$, $CellContext`c$$, $CellContext`d$$], $CellContext`TanEq[$CellContext`x0$$, $CellContext`a$$, \ $CellContext`b$$, $CellContext`c$$, $CellContext`d$$]], "\[Ellipsis]"]}], 16]]], Manipulate`Dump`ThisIsNotAControl}}, Typeset`size$$ = { 456., {261., 302.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`rationalize$17287$$ = False, $CellContext`a$17288$$ = 0, $CellContext`b$17289$$ = 0, $CellContext`c$17290$$ = 0, $CellContext`d$17291$$ = 0, $CellContext`firstD$17292$$ = False, $CellContext`secondD$17293$$ = False, $CellContext`xx$17294$$ = False, $CellContext`yy$17295$$ = False, $CellContext`origin$17296$$ = False, $CellContext`tangent$17297$$ = False, $CellContext`x0$17298$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 2, StandardForm, "Variables" :> {$CellContext`a$$ = 1, $CellContext`b$$ = 1, $CellContext`c$$ = 0, $CellContext`d$$ = 0, $CellContext`firstD$$ = False, $CellContext`origin$$ = False, $CellContext`rationalize$$ = True, $CellContext`secondD$$ = False, $CellContext`tangent$$ = False, $CellContext`x0$$ = 0, $CellContext`xx$$ = False, $CellContext`yy$$ = False}, "ControllerVariables" :> { Hold[$CellContext`rationalize$$, $CellContext`rationalize$17287$$, False], Hold[$CellContext`a$$, $CellContext`a$17288$$, 0], Hold[$CellContext`b$$, $CellContext`b$17289$$, 0], Hold[$CellContext`c$$, $CellContext`c$17290$$, 0], Hold[$CellContext`d$$, $CellContext`d$17291$$, 0], Hold[$CellContext`firstD$$, $CellContext`firstD$17292$$, False], Hold[$CellContext`secondD$$, $CellContext`secondD$17293$$, False], Hold[$CellContext`xx$$, $CellContext`xx$17294$$, False], Hold[$CellContext`yy$$, $CellContext`yy$17295$$, False], Hold[$CellContext`origin$$, $CellContext`origin$17296$$, False], Hold[$CellContext`tangent$$, $CellContext`tangent$17297$$, False], Hold[$CellContext`x0$$, $CellContext`x0$17298$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Labeled[ DynamicModule[{$CellContext`p = {0, $CellContext`f[ 0, $CellContext`a$$, $CellContext`b$$, $CellContext`c$$, \ $CellContext`d$$]}}, LocatorPane[ Dynamic[$CellContext`p], Plot[{ $CellContext`f[$CellContext`x, $CellContext`a$$, \ $CellContext`b$$, $CellContext`c$$, $CellContext`d$$], If[$CellContext`firstD$$, $CellContext`Df[$CellContext`x, $CellContext`a$$, \ $CellContext`b$$, $CellContext`c$$, $CellContext`d$$]], If[$CellContext`secondD$$, $CellContext`DDf[$CellContext`x, $CellContext`a$$, \ $CellContext`b$$, $CellContext`c$$, $CellContext`d$$]], If[$CellContext`xx$$, -$CellContext`f[$CellContext`x, \ $CellContext`a$$, $CellContext`b$$, $CellContext`c$$, $CellContext`d$$]], If[$CellContext`yy$$, $CellContext`f[-$CellContext`x, $CellContext`a$$, \ $CellContext`b$$, $CellContext`c$$, $CellContext`d$$]], If[$CellContext`origin$$, -$CellContext`f[-$CellContext`x, \ $CellContext`a$$, $CellContext`b$$, $CellContext`c$$, $CellContext`d$$]], If[$CellContext`tangent$$, $CellContext`f[$CellContext`x0$$, \ $CellContext`a$$, $CellContext`b$$, $CellContext`c$$, $CellContext`d$$] + \ $CellContext`Df[$CellContext`x0$$, $CellContext`a$$, $CellContext`b$$, \ $CellContext`c$$, $CellContext`d$$] ($CellContext`x - $CellContext`x0$$)]}, \ {$CellContext`x, $CellContext`xmin, $CellContext`xmax}, PlotRange -> 12, AspectRatio -> Automatic, AxesLabel -> {$CellContext`x, "y"}, Ticks -> {{(-3) Pi, (-2) Pi, -Pi, 0, Pi, 2 Pi, 3 Pi}, Automatic}, GridLines -> { Table[$CellContext`i, {$CellContext`i, (-3) Pi, 3 Pi, Pi/2}], Table[$CellContext`i, {$CellContext`i, -10, 10, 2}]}, GridLinesStyle -> Directive[LightGray, Dashed], ImageSize -> 450, Epilog -> { Locator[ Dynamic[{ First[$CellContext`p], $CellContext`f[ First[$CellContext`p], $CellContext`a$$, $CellContext`b$$, \ $CellContext`c$$, $CellContext`d$$]}], ImageSize -> 12], Inset[ Framed[ Column[{ Style["Plot Functions", 13], Row[{ Style[ " \!\(\*\nStyleBox[\"\[LongDash]\",\nFontSize->24]\)", ColorData[54][17]], " \!\(\*\nStyleBox[\"f\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"(\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"x\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\")\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)"}], If[$CellContext`firstD$$, Row[{ Style[ " \!\(\*\nStyleBox[\"\[LongDash]\",\nFontSize->24]\)", ColorData[54][8]], " \!\(\*\nStyleBox[\"f\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"'\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"(\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"x\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\")\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)"}]], If[$CellContext`secondD$$, Row[{ Style[ " \!\(\*\nStyleBox[\"\[LongDash]\",\nFontSize->24]\)", ColorData[54][2]], " \!\(\*\nStyleBox[\"f\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"''\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"(\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"x\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\")\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)"}]], If[$CellContext`xx$$, Row[{ Style[ " \!\(\*\nStyleBox[\"\[LongDash]\",\nFontSize->24]\)", ColorData[54][9]], " \!\(\*\nStyleBox[\"-\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"f\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"(\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"x\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\")\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)"}]], If[$CellContext`yy$$, Row[{ Style[ " \!\(\*\nStyleBox[\"\[LongDash]\",\nFontSize->24]\)", ColorData[54][14]], " \!\(\*\nStyleBox[\"f\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"(\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"-\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"x\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\")\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)"}]], If[$CellContext`origin$$, Row[{ Style[ " \!\(\*\nStyleBox[\"\[LongDash]\",\nFontSize->24]\)", ColorData[54][11]], " \!\(\*\nStyleBox[\"-\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"f\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"(\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"-\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"x\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\")\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)"}]], If[$CellContext`tangent$$, Row[{ Style[ " \!\(\*\nStyleBox[\"\[LongDash]\",\nFontSize->24]\)", ColorData[54][6]], " \!\(\*\nStyleBox[\"Tangent\",\nFontSize->14,\n\ FontSlant->\"Italic\"]\)"}]]}], Background -> LightGreen, RoundingRadius -> 5, FrameStyle -> {Gray, Thin}], {-8.2, -8.3}], Inset[ Framed[ Style[ Column[{"Coordinates", Row[{"\!\(\*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)\ \!\(\*\nStyleBox[\"x\",\nFontSlant->\"Italic\"]\)", " = ", Dynamic[ Part[$CellContext`p, 1]], " "}], Row[{" \!\(\*\nStyleBox[\"y\",\n\ FontSlant->\"Italic\"]\)", " \[TildeEqual] ", Dynamic[ Part[$CellContext`p, 2]], " "}]}], 13], Background -> ColorData[35][4], RoundingRadius -> 5, FrameStyle -> {Gray, Thin}], {7.5, -10}]}, PlotStyle -> {{ ColorData[54][17], Thick}, { ColorData[54][8], Thick}, { ColorData[54][2], Thick}, { ColorData[54][9], Thick}, { ColorData[54][14], Thick}, { ColorData[54][11], Thick}, { ColorData[54][6]}}], Appearance -> None]], Framed[ Style[ " \!\(\*\nStyleBox[\"F\",\nFontSize->24,\n\ FontColor->RGBColor[0.14233615625238422`, 0.4197146562905318, 0.]]\)\!\(\*\n\ StyleBox[\"-\",\nFontSize->24,\nFontColor->RGBColor[0.14233615625238422`, \ 0.4197146562905318, 0.]]\)\!\(\*\nStyleBox[\"Cosine\",\nFontSize->24,\n\ FontColor->RGBColor[0.14233615625238422`, 0.4197146562905318, 0.]]\)\!\(\*\n\ StyleBox[\":\",\nFontSize->24,\nFontColor->RGBColor[0.14233615625238422`, \ 0.4197146562905318, 0.]]\)\!\(\*\nStyleBox[\" \",\nFontSize->18,\n\ FontColor->RGBColor[0.14233615625238422`, 0.4197146562905318, 0.]]\)\!\(\*\n\ StyleBox[\"f\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\"(\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\"x\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\")\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\"=\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\" \",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\"a\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\" \",\nFontSize->14,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\"cos\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\"(\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\"b\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\"(\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\"x\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\"-\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\"c\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\")\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\")\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\"+\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\"d\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\(\*\n StyleBox[\" \",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, \ 0.]]\\ \)]\)", Bold], Background -> ColorData[35][3], RoundingRadius -> 5, FrameStyle -> Blue], Top], "Specifications" :> { Style["\!\(\*\nStyleBox[\"Arithmetic\",\nFontSize->14]\)", Bold], "", {{$CellContext`rationalize$$, True, ""}, { True -> "Exact", False -> "Approximate"}}, Delimiter, Style["\!\(\*\nStyleBox[\"Parameters\",\nFontSize->14]\)", Bold], "", {{$CellContext`a$$, 1}, -10, 10, 0.01, ImageSize -> Small, Appearance -> "Labeled"}, {{$CellContext`b$$, 1}, -5, 5, 0.01, ImageSize -> Small, Appearance -> "Labeled"}, {{$CellContext`c$$, 0}, -5, 5, 0.01, ImageSize -> Small, Appearance -> "Labeled"}, {{$CellContext`d$$, 0}, -5, 5, 0.01, ImageSize -> Small, Appearance -> "Labeled"}, Delimiter, Style["\!\(\*\nStyleBox[\"Derivatives\",\nFontSize->14]\)", Bold], "", {{$CellContext`firstD$$, False, Text[ TraditionalForm[ TraditionalForm[ Text[ Style[ Derivative[1][$CellContext`f][$CellContext`x], 16]]]]]}, { True, False}, ControlPlacement -> 1}, {{$CellContext`secondD$$, False, Text[ TraditionalForm[ TraditionalForm[ Text[ Style[ Derivative[2][$CellContext`f][$CellContext`x], 16]]]]]}, { True, False}, ControlPlacement -> 2}, Row[{" ", Manipulate`Place[1], " ", Row[{ Manipulate`Place[2]}], " "}], Delimiter, Style["\!\(\*\nStyleBox[\"Symmetry\",\nFontSize->14]\)", Bold], "", " \!\(\*\nStyleBox[\"X\",\nFontSize->14]\)\!\(\*\nStyleBox[\"-\",\n\ FontSize->14]\)\!\(\*\nStyleBox[\"Axis\",\nFontSize->14]\)\!\(\*\n\ StyleBox[\":\",\nFontSize->14]\)", {{$CellContext`xx$$, False, Text[ TraditionalForm[ TraditionalForm[ Text[ Style[ Row[{-$CellContext`f[$CellContext`x], " "}], 16]]]]]}, { True, False}, ControlPlacement -> 3}, Row[{" ", Manipulate`Place[3]}], "", " \!\(\*\nStyleBox[\"Y\",\nFontSize->14]\)\!\(\*\nStyleBox[\"-\",\n\ FontSize->14]\)\!\(\*\nStyleBox[\"Axis\",\nFontSize->14]\)\!\(\*\n\ StyleBox[\":\",\nFontSize->14]\)", {{$CellContext`yy$$, False, Text[ TraditionalForm[ TraditionalForm[ Text[ Style[ Row[{ $CellContext`f[-$CellContext`x], " "}], 16]]]]]}, { True, False}, ControlPlacement -> 4}, Row[{" ", Manipulate`Place[4]}], "", " \!\(\*\nStyleBox[\"Axes\",\nFontSize->14]\)\!\(\*\nStyleBox[\" \ \",\nFontSize->14]\)\!\(\*\nStyleBox[\"Origin\",\nFontSize->14]\)\!\(\*\n\ StyleBox[\":\",\nFontSize->14]\)", {{$CellContext`origin$$, False, Text[ TraditionalForm[ TraditionalForm[ Text[ Style[-$CellContext`f[-$CellContext`x], 16]]]]]}, { True, False}, ControlPlacement -> 5}, Row[{" ", Manipulate`Place[5]}], Delimiter, Style[ "\!\(\*\nStyleBox[\"Tangent\",\nFontSize->14]\)\!\(\*\nStyleBox[\" \ \",\nFontSize->14]\)\!\(\*\nStyleBox[\"Line\",\nFontSize->14]\)\!\(\*\n\ StyleBox[\" \",\nFontSize->14]\)\!\(\*\nStyleBox[\"at\",\nFontSize->14]\)\!\(\ \*\nStyleBox[\" \",\nFontSize->14]\)\!\(\*\nStyleBox[SubscriptBox[\"x\", \ \"0\"],\nFontSize->14]\)", Bold], {{$CellContext`tangent$$, False, "\!\(\*\nStyleBox[\"Tangent\",\nFontSize->14,\nFontSlant->\"Italic\ \"]\)\!\(\*\nStyleBox[\" \",\nFontSize->14,\nFontSlant->\"Italic\"]\)\!\(\*\n\ StyleBox[\"Line\",\nFontSize->14,\nFontSlant->\"Italic\"]\)"}, {True, False}, ControlPlacement -> 6}, Row[{" ", Manipulate`Place[6]}], {{$CellContext`x0$$, 0}, -10, 10, 0.01, ImageSize -> Small, Appearance -> "Labeled", ControlPlacement -> 7}, Dynamic[ If[$CellContext`tangent$$, Row[{" ", Manipulate`Place[7]}], ""]], Row[{ Style[ " \!\(\*\nStyleBox[\"Domain\",\nFontSize->14]\)\!\(\*\n\ StyleBox[\" \",\nFontSize->14]\)\!\(\*\nStyleBox[\"=\",\n\ FontSize->14]\)\!\(\*\nStyleBox[\" \",\nFontSize->14]\)", Bold], Style[" \[DoubleStruckCapitalR]", 16]}], "", "", Dynamic[ Style[ Row[ If[$CellContext`a$$ $CellContext`b$$ == 0, { Style[" Range = ", Bold], Style["{", 16], If[$CellContext`rationalize$$, Rationalize[$CellContext`a$$ + $CellContext`d$$], \ $CellContext`a$$ + $CellContext`d$$], Style["}", 16]}, { Style[" Range = ", Bold], Style["[ ", 16], If[$CellContext`rationalize$$, Rationalize[-Abs[$CellContext`a$$] + $CellContext`d$$], - Abs[$CellContext`a$$] + $CellContext`d$$], Style[" ; ", 16], If[$CellContext`rationalize$$, Rationalize[Abs[$CellContext`a$$] + $CellContext`d$$], Abs[$CellContext`a$$] + $CellContext`d$$], Style["]", 16]}]], 14]], Delimiter, Style[" \!\(\*\nStyleBox[\"Zeros\",\nFontSize->14]\)", Bold], "", Dynamic[ If[$CellContext`a$$ $CellContext`b$$ == 0, If[$CellContext`d$$ != -$CellContext`a$$, Style[" No Real Zeros", 14], $CellContext`TradForm[ Row[{" ", TraditionalForm[ Style[$CellContext`x, 16]], "\!\(\*\nStyleBox[\" \",\nFontSize->14]\)\!\(\*\nStyleBox[\"\ \[Element]\",\nFontSize->14]\)\!\(\*\nStyleBox[\" \",\nFontSize->14]\)\!\(\*\n\ StyleBox[\"\[DoubleStruckCapitalR]\",\nFontSize->14]\)\!\(\*\nStyleBox[\" \",\ \nFontSize->14]\)"}], 16]], If[ Or[(-$CellContext`d$$)/$CellContext`a$$ < -1, \ (-$CellContext`d$$)/$CellContext`a$$ > 1], Style[" No Real Zeros", 14], $CellContext`TradForm[ If[$CellContext`rationalize$$, Column[{ Row[{" \!\(\*\nStyleBox[\"x\",\nFontSlant->\"Italic\"]\) \ =\!\(\*\nStyleBox[\" \",\nFontSize->9]\)", ReplaceRepeated[ $CellContext`Zero1[$CellContext`a$$, $CellContext`b$$, \ $CellContext`c$$, $CellContext`d$$], $CellContext`arcFormat], If[$CellContext`b$$ > 0, " + ", " "], If[$CellContext`b$$ == -2, "-", If[$CellContext`b$$ != 2, Rationalize[2/$CellContext`b$$]]], "\!\(\*\nStyleBox[\" \",\nFontSize->9]\)\!\(\*\n\ StyleBox[\"k\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\n\ FontSize->9,\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"\[Pi]\",\n\ FontSlant->\"Italic\"]\)"}], " \[Or] ", Row[{" \!\(\*\nStyleBox[\"x\",\nFontSlant->\"Italic\"]\) \ =\!\(\*\nStyleBox[\" \",\nFontSize->9]\)", ReplaceRepeated[ $CellContext`Zero2[$CellContext`a$$, $CellContext`b$$, \ $CellContext`c$$, $CellContext`d$$], $CellContext`arcFormat], If[$CellContext`b$$ > 0, " + ", " "], If[$CellContext`b$$ == -2, "-", If[$CellContext`b$$ != 2, Rationalize[2/$CellContext`b$$]]], "\!\(\*\nStyleBox[\" \",\nFontSize->9]\)\!\(\*\n\ StyleBox[\"k\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\n\ FontSize->9,\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"\[Pi]\",\n\ FontSlant->\"Italic\"]\), \!\(\*\nStyleBox[\"k\",\n\ FontSlant->\"Italic\"]\) \[Element] \[DoubleStruckCapitalZ] "}]}], Column[{ Row[{" \!\(\*\nStyleBox[\"x\",\nFontSlant->\"Italic\"]\) \ \[TildeEqual]\!\(\*\nStyleBox[\" \",\nFontSize->9]\)", (1/$CellContext`b$$) N[ ArcCos[(-$CellContext`d$$)/$CellContext`a$$]] + \ $CellContext`c$$, If[$CellContext`b$$ > 0, " + ", " "], If[$CellContext`b$$ == -2, "-", If[$CellContext`b$$ != 2, 2/$CellContext`b$$]], "\!\(\*\nStyleBox[\" \",\nFontSize->9]\)\!\(\*\n\ StyleBox[\"k\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\n\ FontSize->9,\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"\[Pi]\",\n\ FontSlant->\"Italic\"]\)"}], " \[Or] ", Row[{" \!\(\*\nStyleBox[\"x\",\nFontSlant->\"Italic\"]\) \ \[TildeEqual]\!\(\*\nStyleBox[\" \",\nFontSize->9]\)", \ ((-1)/$CellContext`b$$) N[ ArcCos[(-$CellContext`d$$)/$CellContext`a$$]] + \ $CellContext`c$$, If[$CellContext`b$$ > 0, " + ", " "], If[$CellContext`b$$ == -2, "-", If[$CellContext`b$$ != 2, 2/$CellContext`b$$]], "\!\(\*\nStyleBox[\" \",\nFontSize->9]\)\!\(\*\n\ StyleBox[\"k\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\n\ FontSize->9,\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"\[Pi]\",\n\ FontSlant->\"Italic\"]\), \!\(\*\nStyleBox[\"k\",\n\ FontSlant->\"Italic\"]\) \[Element] \[DoubleStruckCapitalZ] "}]}]], 16]]]], Delimiter, Style[ " \!\(\*\nStyleBox[\"Extreme\",\nFontSize->14]\)\!\(\*\nStyleBox[\" \ \",\nFontSize->14]\)\!\(\*\nStyleBox[\"Values\",\nFontSize->14]\)\!\(\*\n\ StyleBox[\" \",\nFontSize->14]\)\!\(\*\nStyleBox[\"and\",\n\ FontSize->14]\)\!\(\*\nStyleBox[\" \",\nFontSize->14]\)\!\(\*\n\ StyleBox[\"Critical\",\nFontSize->14]\)\!\(\*\nStyleBox[\" \",\nFontSize->14]\ \)\!\(\*\nStyleBox[\"Points\",\nFontSize->14]\)", Bold], "", Dynamic[ If[$CellContext`a$$ $CellContext`b$$ == 0, $CellContext`TradForm[ If[$CellContext`rationalize$$, Row[{" Min, Max\!\(\*\nStyleBox[\" \",\nFontSize->7]\): \!\ \(\*\nStyleBox[\"y\",\nFontSlant->\"Italic\"]\) = ", Rationalize[$CellContext`a$$ + $CellContext`d$$], " for all \!\(\*\nStyleBox[\"x\",\nFontSlant->\"Italic\"]\) \ \[Element] \[DoubleStruckCapitalR]"}], Row[{" Min, Max\!\(\*\nStyleBox[\" \",\nFontSize->7]\): \!\ \(\*\nStyleBox[\"y\",\nFontSlant->\"Italic\"]\) = ", $CellContext`a$$ + \ $CellContext`d$$, " for all \!\(\*\nStyleBox[\"x\",\nFontSlant->\"Italic\"]\) \ \[Element] \[DoubleStruckCapitalR]"}]], 16], If[$CellContext`c$$ != 0, $CellContext`TradForm[ If[$CellContext`rationalize$$, Column[{ Row[{" Min: \!\(\*\nStyleBox[\"y\",\nFontSlant->\"Italic\ \"]\)\!\(\*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)=\!\(\*\nStyleBox[\" \ \",\nFontSize->9]\)", Rationalize[-$CellContext`a$$ + $CellContext`d$$], " for all \!\(\*\nStyleBox[\"x\",\n\ FontSlant->\"Italic\"]\) = ", Rationalize[$CellContext`c$$] + (Sign[$CellContext`a$$] Rationalize[1/$CellContext`b$$]) Pi, If[$CellContext`b$$ > 0, " + ", " "], If[$CellContext`b$$ == -2, "-", If[$CellContext`b$$ != 2, Rationalize[2/$CellContext`b$$]]], "\!\(\*\nStyleBox[\"k\",\nFontSlant->\"Italic\"]\)\!\(\*\n\ StyleBox[\" \",\nFontSize->9,\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"\ \[Pi]\",\nFontSlant->\"Italic\"]\)"}], Row[{" Max: \!\(\*\nStyleBox[\"y\",\nFontSlant->\"Italic\ \"]\)\!\(\*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)=\!\(\*\nStyleBox[\" \ \",\nFontSize->9]\)", Rationalize[$CellContext`a$$ + $CellContext`d$$], " for all \!\(\*\nStyleBox[\"x\",\n\ FontSlant->\"Italic\"]\) = ", Rationalize[$CellContext`c$$], If[$CellContext`b$$ > 0, " + ", " "], If[$CellContext`b$$ == -2, "-", If[$CellContext`b$$ != 2, Rationalize[2/$CellContext`b$$]]], "\!\(\*\nStyleBox[\"k\",\nFontSlant->\"Italic\"]\)\!\(\*\n\ StyleBox[\" \",\nFontSize->9,\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"\ \[Pi]\",\nFontSlant->\"Italic\"]\), \!\(\*\nStyleBox[\"k\",\n\ FontSlant->\"Italic\"]\) \[Element] \[DoubleStruckCapitalZ] "}]}], Column[{ Row[{" Min: \!\(\*\nStyleBox[\"y\",\nFontSlant->\"Italic\ \"]\)\!\(\*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)\[TildeEqual]\!\(\*\n\ StyleBox[\" \",\nFontSize->9]\)", -$CellContext`a$$ + $CellContext`d$$, " for all \!\(\*\nStyleBox[\"x\",\n\ FontSlant->\"Italic\"]\) \[TildeEqual] ", $CellContext`c$$ + Sign[$CellContext`a$$] (N[Pi]/$CellContext`b$$), If[$CellContext`b$$ > 0, " + ", " "], If[$CellContext`b$$ == -2, "-", If[$CellContext`b$$ != 2, 2/$CellContext`b$$]], "\!\(\*\nStyleBox[\" \",\nFontSize->9]\)\!\(\*\n\ StyleBox[\"k\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\n\ FontSize->9,\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"\[Pi]\",\n\ FontSlant->\"Italic\"]\)"}], Row[{" Max: \!\(\*\nStyleBox[\"y\",\nFontSlant->\"Italic\ \"]\)\!\(\*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)\[TildeEqual]\!\(\*\n\ StyleBox[\" \",\nFontSize->9]\)", $CellContext`a$$ + $CellContext`d$$, " for all \!\(\*\nStyleBox[\"x\",\n\ FontSlant->\"Italic\"]\) \[TildeEqual] ", $CellContext`c$$, If[$CellContext`b$$ > 0, " + ", " "], If[$CellContext`b$$ == -2, "-", If[$CellContext`b$$ != 2, 2/$CellContext`b$$]], "\!\(\*\nStyleBox[\" \",\nFontSize->9]\)\!\(\*\n\ StyleBox[\"k\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\n\ FontSize->9,\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"\[Pi]\",\n\ FontSlant->\"Italic\"]\), \!\(\*\nStyleBox[\"k\",\n\ FontSlant->\"Italic\"]\) \[Element] \[DoubleStruckCapitalZ] "}]}]], 16], $CellContext`TradForm[ If[$CellContext`rationalize$$, Column[{ Row[{" Min: \!\(\*\nStyleBox[\"y\",\nFontSlant->\"Italic\ \"]\)\!\(\*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)=\!\(\*\nStyleBox[\" \ \",\nFontSize->9]\)", Rationalize[-$CellContext`a$$ + $CellContext`d$$], " for all \!\(\*\nStyleBox[\"x\",\n\ FontSlant->\"Italic\"]\) = ", (Sign[$CellContext`a$$] Rationalize[1/$CellContext`b$$]) Pi, If[$CellContext`b$$ > 0, " + ", " "], If[$CellContext`b$$ == -2, "-", If[$CellContext`b$$ != 2, Rationalize[2/$CellContext`b$$]]], "\!\(\*\nStyleBox[\"k\",\nFontSlant->\"Italic\"]\)\!\(\*\n\ StyleBox[\" \",\nFontSize->9,\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"\ \[Pi]\",\nFontSlant->\"Italic\"]\)"}], Row[{" Max: \!\(\*\nStyleBox[\"y\",\nFontSlant->\"Italic\ \"]\)\!\(\*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)=\!\(\*\nStyleBox[\" \ \",\nFontSize->9]\)", Rationalize[$CellContext`a$$ + $CellContext`d$$], " for all \!\(\*\nStyleBox[\"x\",\n\ FontSlant->\"Italic\"]\) = ", If[$CellContext`b$$ == -2, "-", If[$CellContext`b$$ != 2, Rationalize[2/$CellContext`b$$]]], "\!\(\*\nStyleBox[\"k\",\nFontSlant->\"Italic\"]\)\!\(\*\n\ StyleBox[\" \",\nFontSize->9,\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"\ \[Pi]\",\nFontSlant->\"Italic\"]\), \!\(\*\nStyleBox[\"k\",\n\ FontSlant->\"Italic\"]\) \[Element] \[DoubleStruckCapitalZ] "}]}], Column[{ Row[{" Min: \!\(\*\nStyleBox[\"y\",\nFontSlant->\"Italic\ \"]\)\!\(\*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)\[TildeEqual]\!\(\*\n\ StyleBox[\" \",\nFontSize->9]\)", -$CellContext`a$$ + $CellContext`d$$, " for all \!\(\*\nStyleBox[\"x\",\n\ FontSlant->\"Italic\"]\) \[TildeEqual] ", Sign[$CellContext`a$$] (N[Pi]/$CellContext`b$$), If[$CellContext`b$$ > 0, " + ", " "], If[$CellContext`b$$ == -2, "-", If[$CellContext`b$$ != 2, 2/$CellContext`b$$]], "\!\(\*\nStyleBox[\" \",\nFontSize->9]\)\!\(\*\n\ StyleBox[\"k\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\n\ FontSize->9,\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"\[Pi]\",\n\ FontSlant->\"Italic\"]\)"}], Row[{" Max: \!\(\*\nStyleBox[\"y\",\nFontSlant->\"Italic\ \"]\)\!\(\*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)\[TildeEqual]\!\(\*\n\ StyleBox[\" \",\nFontSize->9]\)", $CellContext`a$$ + $CellContext`d$$, " for all \!\(\*\nStyleBox[\"x\",\n\ FontSlant->\"Italic\"]\) \[TildeEqual] ", If[$CellContext`b$$ == -2, "-", If[$CellContext`b$$ != 2, 2/$CellContext`b$$]], "\!\(\*\nStyleBox[\" \",\nFontSize->9]\)\!\(\*\n\ StyleBox[\"k\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\n\ FontSize->9,\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"\[Pi]\",\n\ FontSlant->\"Italic\"]\), \!\(\*\nStyleBox[\"k\",\n\ FontSlant->\"Italic\"]\) \[Element] \[DoubleStruckCapitalZ] "}]}]], 16]]]], Delimiter, Style[ " \!\(\*\nStyleBox[\"Inflection\",\nFontSize->14]\)\!\(\*\n\ StyleBox[\" \",\nFontSize->14]\)\!\(\*\nStyleBox[\"Points\",\n\ FontSize->14]\)", Bold], "", Dynamic[ If[$CellContext`a$$ $CellContext`b$$ == 0, $CellContext`TradForm[ Row[{" No Inflection Points"}], 16], If[$CellContext`c$$ - Pi/2 != 0, $CellContext`TradForm[ If[$CellContext`rationalize$$, Row[{" \!\(\*\nStyleBox[\"y\",\nFontSlant->\"Italic\"]\)\!\ \(\*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)=\!\(\*\nStyleBox[\" \",\n\ FontSize->9]\)", Rationalize[$CellContext`d$$], " for all \!\(\*\nStyleBox[\"x\",\n\ FontSlant->\"Italic\"]\) = ", Rationalize[$CellContext`c$$] - Pi/2, If[$CellContext`b$$ > 0, " + ", " "], If[$CellContext`b$$ == -1, "-", 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Right, Right, Right, Right, Right, Right, Right, Right, Right, Right, Right, Right, Right, Right, Right}}, "DefaultOptions" :> {}], ImageSizeCache->{963., {307., 313.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>({$CellContext`f[ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`a, Blank[]], Pattern[$CellContext`b, Blank[]], Pattern[$CellContext`c, Blank[]], Pattern[$CellContext`d, Blank[]]] = $CellContext`d + $CellContext`a Cos[$CellContext`b (-$CellContext`c + $CellContext`x)], \ $CellContext`Df[ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`a, Blank[]], Pattern[$CellContext`b, Blank[]], Pattern[$CellContext`c, Blank[]], Pattern[$CellContext`d, Blank[]]] = -(($CellContext`a $CellContext`b) Sin[$CellContext`b (-$CellContext`c + $CellContext`x)]), \ $CellContext`DDf[ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`a, Blank[]], Pattern[$CellContext`b, Blank[]], Pattern[$CellContext`c, Blank[]], Pattern[$CellContext`d, Blank[]]] = -(($CellContext`a $CellContext`b^2) Cos[$CellContext`b (-$CellContext`c + $CellContext`x)]), \ $CellContext`xmin = -10, $CellContext`xmax = 10, Attributes[Derivative] = { NHoldAll, ReadProtected}, $CellContext`TradForm[ Pattern[$CellContext`arg, Blank[]], Pattern[$CellContext`size, Blank[]]] = Text[ TraditionalForm[ TraditionalForm[ Text[ Style[$CellContext`arg, $CellContext`size]]]]], \ $CellContext`Zero1[ Pattern[$CellContext`a, Blank[]], Pattern[$CellContext`b, Blank[]], Pattern[$CellContext`c, Blank[]], Pattern[$CellContext`d, Blank[]]] := Rationalize[1/$CellContext`b] ArcCos[ Rationalize[(-$CellContext`d)/$CellContext`a]] + Rationalize[$CellContext`c], $CellContext`arcFormat = ArcSin -> Superscript[$CellContext`sin, -1], Attributes[Superscript] = { NHoldRest, ReadProtected}, $CellContext`Zero2[ Pattern[$CellContext`a, Blank[]], Pattern[$CellContext`b, Blank[]], Pattern[$CellContext`c, Blank[]], Pattern[$CellContext`d, Blank[]]] := Rationalize[(-1)/$CellContext`b] ArcCos[ Rationalize[(-$CellContext`d)/$CellContext`a]] + Rationalize[$CellContext`c], $CellContext`Rf[ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`a, Blank[]], Pattern[$CellContext`b, Blank[]], Pattern[$CellContext`c, Blank[]], Pattern[$CellContext`d, Blank[]]] := Rationalize[$CellContext`a] Cos[Rationalize[$CellContext`b] ($CellContext`x - Rationalize[$CellContext`c])] + Rationalize[$CellContext`d], $CellContext`RDf[ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`a, Blank[]], Pattern[$CellContext`b, Blank[]], Pattern[$CellContext`c, Blank[]], Pattern[$CellContext`d, Blank[]]] := (-Rationalize[$CellContext`a $CellContext`b]) Sin[Rationalize[$CellContext`b] ($CellContext`x - Rationalize[$CellContext`c])], $CellContext`RDDf[ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`a, Blank[]], Pattern[$CellContext`b, Blank[]], Pattern[$CellContext`c, Blank[]], Pattern[$CellContext`d, Blank[]]] := (-Rationalize[$CellContext`a $CellContext`b^2]) Cos[Rationalize[$CellContext`b] ($CellContext`x - Rationalize[$CellContext`c])], $CellContext`TanEqR[ Pattern[$CellContext`x0, Blank[]], Pattern[$CellContext`a, Blank[]], Pattern[$CellContext`b, Blank[]], Pattern[$CellContext`c, Blank[]], Pattern[$CellContext`d, Blank[]]] := Expand[ FullSimplify[$CellContext`Rf[ Rationalize[$CellContext`x0], $CellContext`a, $CellContext`b, \ $CellContext`c, $CellContext`d] + $CellContext`RDf[ Rationalize[$CellContext`x0], $CellContext`a, $CellContext`b, \ $CellContext`c, $CellContext`d] ($CellContext`x - Rationalize[$CellContext`x0])]], $CellContext`TanEq[ Pattern[$CellContext`x0, Blank[]], Pattern[$CellContext`a, Blank[]], Pattern[$CellContext`b, Blank[]], Pattern[$CellContext`c, Blank[]], Pattern[$CellContext`d, Blank[]]] = $CellContext`d + $CellContext`a Cos[$CellContext`b (-$CellContext`c + $CellContext`x0)] - \ (($CellContext`a $CellContext`b) $CellContext`x) Sin[$CellContext`b (-$CellContext`c + $CellContext`x0)] + \ (($CellContext`a $CellContext`b) $CellContext`x0) Sin[$CellContext`b (-$CellContext`c + $CellContext`x0)]}; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]}]], "Input"] }, WindowSize->{1280, 682}, WindowMargins->{{0, Automatic}, {Automatic, 2}}, Visible->True, ScrollingOptions->{"VerticalScrollRange"->Fit}, PrivateNotebookOptions->{"VersionedStylesheet"->{"Default.nb"[8.] -> False}}, ShowCellBracket->False, ShowSelection->True, Deployed->True, CellContext->Notebook, TrackCellChangeTimes->False, FrontEndVersion->"9.0 for Mac OS X x86 (32-bit, 64-bit Kernel) (January 25, \ 2013)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[1463, 33, 79832, 1611, 735, "Input"] } ] *) (* End of internal cache information *) (* NotebookSignature Xu0NJooXgf@JWCK2reXpF8rZ *)