(* 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. 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\!\(\*\nStyleBox[\"!\",\nFontSlant->\"Italic\"]\)"], 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$$, If[$CellContext`b$$ != 0, Row[{" -\!\(\*\nStyleBox[\"f\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"(\",\nFontSlant->\"Italic\"]\)\!\(\ \*\nStyleBox[\"-\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"x\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\")\",\nFontSlant->\"Italic\"]\)", If[$CellContext`rationalize$$, " = ", " \[TildeEqual] "], ReplaceAll[ 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$$]], \ $CellContext`lnFormat]}], " -\!\(\*\nStyleBox[\"f\",\nFontSlant->\"Italic\"]\)\!\(\*\n\ StyleBox[\"(\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"-\",\nFontSlant->\ \"Italic\"]\)\!\(\*\nStyleBox[\"x\",\nFontSlant->\"Italic\"]\)\!\(\*\n\ StyleBox[\")\",\nFontSlant->\"Italic\"]\) \!\(\*\nStyleBox[\"does\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)\!\(\ \*\nStyleBox[\"not\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"exist\",\nFontSlant->\"Italic\"]\)\ \!\(\*\nStyleBox[\"!\",\nFontSlant->\"Italic\"]\)"], Row[{" -\!\(\*\nStyleBox[\"f\",\nFontSlant->\"Italic\"]\)\!\(\*\ \nStyleBox[\"(\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"-\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"x\",\nFontSlant->\"Italic\"]\)\!\(\ \*\nStyleBox[\")\",\nFontSlant->\"Italic\"]\)"}]], 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[ $CellContext`TradForm[ If[$CellContext`tangent$$, If[$CellContext`b$$ != 0, Row[{" \!\(\*\nStyleBox[\"y\",\nFontSlant->\"Italic\"]\)", If[$CellContext`rationalize$$, " = ", " \[TildeEqual] "], ReplaceAll[ 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$$]], \ $CellContext`lnFormat]}], " \!\(\*\nStyleBox[\"Tangent\",\nFontSlant->\"Italic\"]\)\!\(\*\n\ StyleBox[\" \",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"Line\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)\!\(\ \*\nStyleBox[\"does\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"not\",\nFontSlant->\"Italic\"]\)\!\ \(\*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"exist\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"!\",\nFontSlant->\"Italic\"]\)"], Row[{" \!\(\*\nStyleBox[\"y\",\nFontSlant->\"Italic\"]\)", If[$CellContext`rationalize$$, " = ", " \[TildeEqual] "], "\[Ellipsis]"}]], 16]]], Manipulate`Dump`ThisIsNotAControl}}, Typeset`size$$ = {496., {261., 302.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`rationalize$5753$$ = False, $CellContext`a$5754$$ = 0, $CellContext`b$5755$$ = 0, $CellContext`c$5756$$ = 0, $CellContext`d$5757$$ = 0, $CellContext`firstD$5758$$ = False, $CellContext`secondD$5759$$ = False, $CellContext`inverse$5760$$ = False, $CellContext`xx$5761$$ = False, $CellContext`yy$5762$$ = False, $CellContext`origin$5763$$ = False, $CellContext`tangent$5764$$ = False, $CellContext`x0$5765$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 2, StandardForm, "Variables" :> {$CellContext`a$$ = 1, $CellContext`b$$ = 1, $CellContext`c$$ = 0, $CellContext`d$$ = 0, $CellContext`firstD$$ = False, $CellContext`inverse$$ = False, $CellContext`origin$$ = False, $CellContext`rationalize$$ = True, $CellContext`secondD$$ = False, $CellContext`tangent$$ = False, $CellContext`x0$$ = $CellContext`c$$ + Sign[$CellContext`b$$], $CellContext`xx$$ = False, $CellContext`yy$$ = False}, "ControllerVariables" :> { Hold[$CellContext`rationalize$$, $CellContext`rationalize$5753$$, False], Hold[$CellContext`a$$, $CellContext`a$5754$$, 0], Hold[$CellContext`b$$, $CellContext`b$5755$$, 0], Hold[$CellContext`c$$, $CellContext`c$5756$$, 0], Hold[$CellContext`d$$, $CellContext`d$5757$$, 0], Hold[$CellContext`firstD$$, $CellContext`firstD$5758$$, False], Hold[$CellContext`secondD$$, $CellContext`secondD$5759$$, False], Hold[$CellContext`inverse$$, $CellContext`inverse$5760$$, False], Hold[$CellContext`xx$$, $CellContext`xx$5761$$, False], Hold[$CellContext`yy$$, $CellContext`yy$5762$$, False], Hold[$CellContext`origin$$, $CellContext`origin$5763$$, False], Hold[$CellContext`tangent$$, $CellContext`tangent$5764$$, False], Hold[$CellContext`x0$$, $CellContext`x0$5765$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Labeled[ If[$CellContext`b$$ != 0, DynamicModule[{$CellContext`p = {$CellContext`c$$ + 1/$CellContext`b$$, $CellContext`d$$}}, LocatorPane[ Dynamic[$CellContext`p], Plot[{ $CellContext`f[$CellContext`x, $CellContext`a$$, \ $CellContext`b$$, $CellContext`c$$, $CellContext`d$$], If[$CellContext`firstD$$, Which[$CellContext`b$$ ($CellContext`x - $CellContext`c$$) > 0, $CellContext`Df[$CellContext`x, $CellContext`a$$, \ $CellContext`b$$, $CellContext`c$$, $CellContext`d$$]]], If[$CellContext`secondD$$, Which[$CellContext`b$$ ($CellContext`x - $CellContext`c$$) > 0, $CellContext`DDf[$CellContext`x, $CellContext`a$$, \ $CellContext`b$$, $CellContext`c$$, $CellContext`d$$]]], If[ And[$CellContext`inverse$$, $CellContext`a$$ != 0, $CellContext`b$$ != 0], $CellContext`invF[$CellContext`x, $CellContext`a$$, \ $CellContext`b$$, $CellContext`c$$, $CellContext`d$$]], If[ And[$CellContext`inverse$$, $CellContext`a$$ != 0, $CellContext`b$$ != 0], $CellContext`x], If[$CellContext`xx$$, -$CellContext`f[$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"}, GridLines -> { Table[$CellContext`i, {$CellContext`i, -10, 10, 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[ And[$CellContext`inverse$$, $CellContext`a$$ != 0, $CellContext`b$$ != 0], Row[{ Style[ " \!\(\*\nStyleBox[\"\[LongDash]\",\nFontSize->24]\)", ColorData[54][15]], " \!\(\*\nStyleBox[SuperscriptBox[\n StyleBox[\"f\",\n\ FontSize->16,\nFontSlant->\"Italic\"], \n RowBox[{\"-\", \"1\"}]],\n\ FontSize->16,\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"(\",\nFontSize->16,\ \nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"x\",\nFontSize->16,\nFontSlant->\ \"Italic\"]\)\!\(\*\nStyleBox[\")\",\nFontSize->16,\n\ FontSlant->\"Italic\"]\)"}]], 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, -7.8}], Inset[ Framed[ Style[ Column[{"Coordinates", Row[{"\!\(\*\nStyleBox[\" \",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"x\",\nFontSlant->\"Italic\"]\)", " = ", Dynamic[ Part[$CellContext`p, 1]], " "}], Row[{" \!\(\*\nStyleBox[\"y\",\nFontSlant->\"Italic\"]\ \)", " \[TildeEqual] ", Dynamic[ Part[$CellContext`p, 2]], " "}]}], 13], Background -> ColorData[35][4], RoundingRadius -> 5, FrameStyle -> {Gray, Thin}], {7.5, -10}]}, PlotStyle -> {{ ColorData[54][17], Thick}, { ColorData[54][8], Thick}, { ColorData[54][2], Thick}, { ColorData[54][15], Thick}, {Black, Dashed}, { ColorData[54][9], Thick}, { ColorData[54][14], Thick}, { ColorData[54][11], Thick}, { ColorData[54][6]}}], Appearance -> None]], Speak["Sorry. You cannot do that!"]; Plot[0, {$CellContext`x, $CellContext`xmin, $CellContext`xmax}, PlotRange -> 12, AspectRatio -> Automatic, AxesLabel -> {$CellContext`x, "y"}, GridLines -> { Table[$CellContext`i, {$CellContext`i, -10, 10, 2}], Table[$CellContext`i, {$CellContext`i, -10, 10, 2}]}, GridLinesStyle -> Directive[LightGray, Dashed], ImageSize -> 450, Epilog -> Inset[$CellContext`CautionImage, {0, 0}]]], Framed[ Style[ " \!\(\*\nStyleBox[\"F\",\nFontSize->24,\n\ FontColor->RGBColor[0.14233615625238422`, 0.4197146562905318, 0.]]\)\!\(\*\n\ StyleBox[\"-\",\nFontSize->24,\nFontColor->RGBColor[0.14233615625238422`, \ 0.4197146562905318, 0.]]\)\!\(\*\nStyleBox[\"Logarithm\",\nFontSize->24,\n\ FontColor->RGBColor[0.14233615625238422`, 0.4197146562905318, 0.]]\)\!\(\*\n\ StyleBox[\":\",\nFontSize->24,\nFontColor->RGBColor[0.14233615625238422`, \ 0.4197146562905318, 0.]]\)\!\(\*\nStyleBox[\" \",\nFontSize->18,\n\ FontColor->RGBColor[0.14233615625238422`, 0.4197146562905318, 0.]]\)\!\(\*\n\ StyleBox[\"f\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\"(\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\"x\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\")\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\"=\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\" \",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\"a\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\" \",\nFontSize->10,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\"ln\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\"(\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\"b\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\"(\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\"x\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\"-\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\"c\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\")\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\")\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\"+\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\"d\",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\)\!\(\*\n\ StyleBox[\" \",\nFontSize->24,\nFontColor->RGBColor[0.4, 0.2, 0.]]\) ", 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$$, 1}, -5, 5, 0.01, ImageSize -> Small, Appearance -> "Labeled"}, {{$CellContext`b$$, 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[ "\!\(\*\nStyleBox[\"Inverse\",\nFontSize->14]\)\!\(\*\nStyleBox[\" \ \",\nFontSize->14]\)\!\(\*\nStyleBox[\"Function\",\nFontSize->14]\)", Bold], "", {{$CellContext`inverse$$, False, Text[ TraditionalForm[ TraditionalForm[ Text[ Style[ Superscript[$CellContext`f, -1][$CellContext`x], 16]]]]]}, { True, False}, ControlPlacement -> 3}, Row[{" ", Manipulate`Place[3]}], 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 -> 4}, Row[{" ", Manipulate`Place[4]}], "", " \!\(\*\nStyleBox[\"Y\",\nFontSize->14]\)\!\(\*\nStyleBox[\"-\",\n\ FontSize->14]\)\!\(\*\nStyleBox[\"Axis\",\nFontSize->14]\)\!\(\*\n\ StyleBox[\":\",\nFontSize->14]\)", {{$CellContext`yy$$, False, Text[ TraditionalForm[ TraditionalForm[ Text[ Style[ Row[{ $CellContext`f[-$CellContext`x], " "}], 16]]]]]}, { True, False}, ControlPlacement -> 5}, Row[{" ", Manipulate`Place[5]}], "", " \!\(\*\nStyleBox[\"Axes\",\nFontSize->14]\)\!\(\*\nStyleBox[\" \ \",\nFontSize->14]\)\!\(\*\nStyleBox[\"Origin\",\nFontSize->14]\)\!\(\*\n\ StyleBox[\":\",\nFontSize->14]\)", {{$CellContext`origin$$, False, Text[ TraditionalForm[ TraditionalForm[ Text[ Style[-$CellContext`f[-$CellContext`x], 16]]]]]}, { True, False}, ControlPlacement -> 6}, Row[{" ", Manipulate`Place[6]}], 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 -> 7}, Row[{" ", Manipulate`Place[7]}], {{$CellContext`x0$$, $CellContext`c$$ + Sign[$CellContext`b$$]}, Dynamic[ If[$CellContext`b$$ < 0, $CellContext`xmin, $CellContext`c$$ + 0.01]], Dynamic[ If[$CellContext`b$$ < 0, $CellContext`c$$ - 0.01, $CellContext`xmax]], 0.01, ImageSize -> Small, Appearance -> "Labeled", ControlPlacement -> 8}, Dynamic[ If[$CellContext`tangent$$, Row[{" ", Manipulate`Place[8]}], ""]], Dynamic[ Style[ Row[ If[$CellContext`b$$ != 0, If[$CellContext`a$$ == 0, { Style[ " Domain = \!\(\*\nStyleBox[\"\[DoubleStruckCapitalR]\",\n\ FontSize->14]\)", Bold]}, If[$CellContext`b$$ < 0, { Style[" Domain = ", Bold], Style["]-\[Infinity]; ", 16], If[$CellContext`rationalize$$, Rationalize[$CellContext`c$$], $CellContext`c$$], Style["[", 16]}, If[$CellContext`b$$ > 0, { Style[" Domain = ", Bold], Style["]", 16], If[$CellContext`rationalize$$, Rationalize[$CellContext`c$$], $CellContext`c$$], Style["; +\[Infinity][", 16]}]]], { Style[" Domain", 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\!\(\*\nStyleBox[\"Analytic\",\nFontSize->14]\)\!\(\*\n\ StyleBox[\" \",\nFontSize->14]\)\!\(\*\nStyleBox[\"Expressions\",\n\ FontSize->14]\)", Bold], "", Dynamic[ $CellContext`TradForm[ If[$CellContext`b$$ != 0, Row[{" \!\(\*\nStyleBox[\"f\",\nFontSlant->\"Italic\"]\)\!\(\*\ \nStyleBox[\"(\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"x\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\")\",\nFontSlant->\"Italic\"]\)", If[$CellContext`rationalize$$, " = ", " \[TildeEqual] "], ReplaceAll[ 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$$]], \ $CellContext`lnFormat]}], " \!\(\*\nStyleBox[\"f\",\nFontSlant->\"Italic\"]\)\!\(\*\n\ StyleBox[\"(\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"x\",\nFontSlant->\ \"Italic\"]\)\!\(\*\nStyleBox[\")\",\nFontSlant->\"Italic\"]\) \!\(\*\n\ StyleBox[\"isn\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"'\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"t\",\nFontSlant->\"Italic\"]\)\!\(\ \*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"well\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)\!\(\ \*\nStyleBox[\"defined\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"!\",\n\ FontSlant->\"Italic\"]\)"], 16]], "", "", Dynamic[ $CellContext`TradForm[ If[$CellContext`firstD$$, If[$CellContext`b$$ != 0, 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$$]]}], " \!\(\*\nStyleBox[\"f\.b4\",\nFontSlant->\"Italic\"]\)\!\(\*\ \nStyleBox[\"(\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"x\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\")\",\nFontSlant->\"Italic\"]\) \ \!\(\*\nStyleBox[\"does\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"not\",\nFontSlant->\"Italic\"]\)\!\ \(\*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"exist\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"!\",\nFontSlant->\"Italic\"]\)"], Row[{" \!\(\*\nStyleBox[\"f\.b4\",\nFontSlant->\"Italic\"]\)\!\ \(\*\nStyleBox[\"(\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"x\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\")\",\nFontSlant->\"Italic\"]\)"}]], 16]], "", "", Dynamic[ $CellContext`TradForm[ If[$CellContext`secondD$$, If[$CellContext`b$$ != 0, Row[{" \!\(\*\nStyleBox[\"f\.b4\.b4\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"(\",\nFontSlant->\"Italic\"]\)\!\(\ 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$CellContext`d$$], $CellContext`TanEq[$CellContext`x0$$, $CellContext`a$$, \ $CellContext`b$$, $CellContext`c$$, $CellContext`d$$]], \ $CellContext`lnFormat]}], " \!\(\*\nStyleBox[\"Tangent\",\nFontSlant->\"Italic\"]\)\!\(\*\n\ StyleBox[\" \",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"Line\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)\!\(\ \*\nStyleBox[\"does\",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\" \",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"not\",\nFontSlant->\"Italic\"]\)\!\ \(\*\nStyleBox[\" \",\nFontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"exist\",\n\ FontSlant->\"Italic\"]\)\!\(\*\nStyleBox[\"!\",\nFontSlant->\"Italic\"]\)"], Row[{" \!\(\*\nStyleBox[\"y\",\nFontSlant->\"Italic\"]\)", If[$CellContext`rationalize$$, " = ", " \[TildeEqual] "], "\[Ellipsis]"}]], 16]]}, "Options" :> { ControlPlacement -> { Left, Left, Left, Left, Left, Left, Left, Left, Left, Left, Left, Left, Left, Left, Left, Left, Left, Left, Left, Left, Left, Left, 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Rationalize[$CellContext`a] Log[Rationalize[$CellContext`b] ($CellContext`x - Rationalize[$CellContext`c])] + Rationalize[$CellContext`d], $CellContext`lnFormat = Log -> $CellContext`ln, $CellContext`RDf[ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`a, Blank[]], Pattern[$CellContext`b, Blank[]], Pattern[$CellContext`c, Blank[]], Pattern[$CellContext`d, Blank[]]] := Rationalize[$CellContext`a]/($CellContext`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`x - Rationalize[$CellContext`c])^2, $CellContext`TanEqR[ Pattern[$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], 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