WolframLanguageData example

WolframLanguageData_example.txt

In[3]:= WolframLanguageData["Plot", "DocumentationExampleInputs"]

Out[3]= {"BasicExamples" -> {{Plot[
     Sin[x], {x, 0, 6 Pi}]}, {Plot[{Sin[x], Sin[2 x], Sin[3 x]}, {x, 
      0, 2 Pi}, 
     PlotLegends -> "Expressions"]}, {Plot[{Sin[x], Cos[x]}, {x, 0, 
      2 Pi}, PlotLabels -> "Expressions"]}, {Plot[
     2 Sin[x] + x, {x, 0, 15}, Filling -> Bottom], 
    Plot[{Sin[x] + x/2, Sin[x] + x}, {x, 0, 10}, 
     Filling -> {1 -> {2}}]}, {Plot[
     Evaluate[Table[BesselJ[n, x], {n, 4}]], {x, 0, 10}, 
     Filling -> Axis]}}, 
 "Scope" -> {{Plot[Sin[30 Sin[x]], {x, 0, 10}]}, {Plot[
     1/x, {x, -1, 1}]}, {Plot[Sqrt[x], {x, -1, 1}]}, {Plot[
     Floor[Sqrt[x]], {x, 0, 100}], 
    Plot[Floor[Sqrt[x]], {x, 0, 100}, Exclusions -> None]}, {Grid@
     Table[Plot[Sin[x], {x, 0, 15}, PlotPoints -> pp, 
       MaxRecursion -> mr], {mr, {0, 1, 2}}, {pp, {5, 10}}]}, {{Plot[
      x^4 - x^2 + 1, {x, -2, 2}], 
     Plot[x^4 - x^2 + 1, {x, -2, 2}, 
      PlotRange -> {0, 2}]}}, {\[ScriptCapitalD] = 
      ImplicitRegion[x <= -1 \[Or] x >= 1, {x}];, 
    Plot[Sin[
      x], {x} \[Element] \[ScriptCapitalD]]}, {\[ScriptCapitalD] = 
      MeshRegion[{{-2}, {-1}, {-1/2}, {1/2}, {1}, {2}}, 
       Line[{{1, 2}, {3, 4}, {5, 6}}]];, 
    Plot[x^3 + 1, {x} \[Element] \[ScriptCapitalD]]}, {Plot[
     Abs[Gamma[z]], {z, -4, 8}, ScalingFunctions -> "Log"]}, {Plot[
     Evaluate@Table[Labeled[x^n, x^n], {n, 1, 3}], {x, -3, 3}], 
    Table[Plot[Labeled[Cos[x], Cos[x], p], {x, 0, 2 Pi}, 
      PlotLabel -> p], {p, {Above, Below, Before, 
       After}}]}, {Plot[{Sin[x], Sin[2 x]}, {x, 0, 6}, 
     PlotLabels -> {Sin[x], Sin[2 x]}]}, {Plot[
     Labeled[Sin[x], "sin(x)", 3], {x, 0, 2 \[Pi]}]}, {Plot[
     Labeled[Sin[x], "sin(x)", Scaled[0.25]], {x, 0, 2 \[Pi]}], 
    Plot[Labeled[Sin[x], Sin[x], {Scaled[0.25], Above}], {x, 0, 
      2 \[Pi]}]}, {Plot[{Callout[n^Sin[n], n^Sin[n]], 
      Callout[n, n]}, {n, 0, 20}]}, {Plot[
     Callout[n^Sin[n], "label", Above], {n, 1, 10}], 
    Plot[Callout[n^Sin[n], "label", 2], {n, 1, 10}]}, {Plot[{Sin[x], 
      Cos[x]}, {x, 0, 2 \[Pi]}, 
     PlotLegends -> {Sin[x], Sin[2 x]}]}, {Plot[{Sin[x], 
      Legended[Mean[{Sin[x], Cos[x]}], "average"], Cos[x]}, {x, 0, 
      2 \[Pi]}], 
    Plot[{Sin[x], 
      Legended[Mean[{Sin[x], Cos[x]}], Placed["average", Below]], 
      Cos[x]}, {x, 0, 2 \[Pi]}]}, {Plot[{x^(1/4), x^(3/4), x^(3/2), 
      x^(7/2)}, {x, 0, 2}]}, {Plot[{x^(1/4), x^(3/4), x^(3/2), 
      x^(7/2)}, {x, 0, 2}, 
     PlotStyle -> {Thick, Automatic, Red, Dashed}]}, {Plot[{x^(1/4), 
      x^(3/4), x^(3/2), x^(7/2)}, {x, 0, 2}, 
     PlotStyle -> {Thick, Automatic, Red, Dashed}, 
     PlotLegends -> Automatic]}, {Plot[Sin[x], {x, 0, 2 Pi}, 
     AxesLabel -> {x, y}, PlotLabel -> Sin[x]], 
    Plot[{x, x^2, x^3}, {x, -2, 2}, PlotLabels -> Automatic]}, {Plot[
     Labeled[x^4 - 25 x^2 + 20 x + 15, {"abs max", "abs min", 
       "rel max", "rel min"}, {Above, Below, 0.5, 3.5}], {x, -5, 5}]
    }, {Plot[{Tooltip[Sin[x]], Tooltip[Sin[2 x]]}, {x, 0, 
      2 Pi}]}, {Plot[{Sin[x], Cos[x]}, {x, 0, 2 Pi}, 
     Filling -> Axis]}, {Plot[{Sin[x], Cos[x]}, {x, 0, 2 Pi}, 
     PlotTheme -> "Marketing"]}, {Plot[Sin[x], {x, 0, 2 Pi}, 
     Mesh -> 20]}, {Plot[Sin[x], {x, 0, 2 Pi}, Mesh -> 10, 
     MeshShading -> {Red, None, Blue}]}}, 
 "GeneralizationsExtensions" -> {}, 
 "Options" -> {{{Plot[Sqrt[1 - x^2], {x, 0, 1}], 
     Plot[Sqrt[1 - x^2], {x, 0, 1}, 
      AspectRatio -> Automatic]}}, {Plot[Sinc[x], {x, 0, 10}, 
     Axes -> False]}, {Plot[Sinc[x], {x, 0, 10}, 
     Axes -> {False, True}]}, {Plot[Sinc[u], {u, 0, 10}, 
     AxesLabel -> Automatic]}, {Plot[Sinc[x], {x, 0, 10}, 
     AxesLabel -> {x, Sinc[x]}]}, {Plot[1/(x - 1) + 2, {x, -2, 4}, 
     AxesOrigin -> Automatic]}, {Plot[1/(x - 1) + 2, {x, -2, 4}, 
     AxesOrigin -> {1, 2}]}, {Plot[Sinc[x], {x, 0, 10}, 
     AxesStyle -> {Directive[Thick, Dashed, Red], Blue}]}, {{Plot[
      Im[Zeta[1/2 + I t]], {t, -20, 20}, BaselinePosition -> Axis], 
     Plot[Re[Zeta[1/2 + I t]], {t, -20, 20}, 
      BaselinePosition -> Axis]}}, {Plot[Sin[x]/x^2, {x, -10, 10}, 
     ClippingStyle -> None]}, {Plot[Sin[x]/x^2, {x, -10, 10}, 
     ClippingStyle -> Automatic]}, {Plot[Sin[x]/x^2, {x, -10, 10}, 
     ClippingStyle -> Red]}, {Plot[Sin[x]/x^2, {x, -10, 10}, 
     ClippingStyle -> {Red, Thick}]}, {Plot[Sin[x]/x^2, {x, -10, 10}, 
     ClippingStyle -> Directive[Red, Thick]]}, {{Plot[
      Sinc[x], {x, 0, 10}, ColorFunction -> Function[{x, y}, Hue[y]]],
      Plot[Sinc[x], {x, 0, 10}, 
      ColorFunction -> Function[{x, y}, Hue[x]]]}}, {Plot[
     Sinc[x], {x, 0, 10}, ColorFunction -> "DarkRainbow"]}, {Plot[
     Sinc[x], {x, 0, 10}, 
     ColorFunction -> Function[{x, y}, If[y > 0, Red, Black]], 
     ColorFunctionScaling -> False, PlotStyle -> Thick]}, {Plot[
     Sin[x], {x, 0, 2 Pi}, ColorFunction -> Function[{x, y}, Hue[y]], 
     Filling -> Axis]}, {Plot[Sinc[x], {x, 0, 10}, 
     ColorFunction -> "DarkRainbow", 
     PlotStyle -> Directive[Red, Thick]]}, {Table[
     Plot[Sin[4 Pi x], {x, 0, 1/2}, PlotStyle -> Thick, 
      ColorFunction -> Function[{x, y}, Hue[x]], 
      ColorFunctionScaling -> cf], {cf, {False, True}}]}, {Plot[
     Sinc[x], {x, 0, 10}, 
     ColorFunction -> Function[{x, y}, If[y > 0, Red, Black]], 
     ColorFunctionScaling -> False, PlotStyle -> Thick]}, {Plot[
     Sin[2 x], {x, 0, 2 Pi}, 
     ColorFunction -> Function[{x, y}, Hue[x, 1, Abs[y]]], 
     ColorFunctionScaling -> {True, False}, 
     PlotStyle -> Thick]}, {Plot[Sin[x], {x, 0, 2 Pi}, 
     Epilog -> {PointSize[0.04], Point[{0, 0}], Point[{Pi, 0}], 
       Point[{2 Pi, 0}]}]}, {Plot[Floor[x], {x, -2, 3}, 
     Epilog -> {Table[Disk[{i, i}, Offset[2.]], {i, -2, 2}], 
       Table[{EdgeForm[Black], White, 
         Disk[{i + 1, i}, Offset[2]]}, {i, -2, 2}]}]}, {Reap[
      Plot[Sin[x], {x, 0, 10}, EvaluationMonitor :> Sow[x]];] // 
     Short}, {data = 
      Reap[ Plot[ Sin[x], {x, 0, 2 Pi}, 
         EvaluationMonitor :> Sow[{x, Sin[x]}]] ][[-1, 1]];, 
    ListPlot[data , Filling -> Axis]}, {Block[{k = 0}, 
     Plot[Sin[x], {x, 0, 2 Pi}, EvaluationMonitor :> k++]; k]}, {Plot[
     Floor[x^2], {x, 0, 5}]}, {Plot[
     Im[Sqrt[-1 + I (y + 1)]], {y, -2, 0}]}, {Plot[
     Im[Sqrt[-1 + I (y + 1)]], {y, -2, 0}, 
     Exclusions -> None]}, {Plot[Tan[x], {x, -2, 2}, 
     Exclusions -> {-Pi/2, Pi/2}]}, {Plot[1/(x^3 - x + 1), {x, -2, 2},
      Exclusions -> {x^3 - x + 1 == 0}]}, {Plot[
     Tan[x^3 - x + 1] + 1/(x + 3 Exp[x]), {x, -2, 2}, 
     Exclusions -> {Cos[x^3 - x + 1] == 0, 
       x + 3 Exp[x] == 0}]}, {Plot[Floor[Tan[x]], {x, -2, 2}, 
     Exclusions -> {Automatic, Cos[x] == 0}]}, {Plot[
     Tan[x], {x, 0, 10}, Exclusions -> {Cos[x] == 0}, 
     ExclusionsStyle -> Dashing[Small]]}, {Plot[Floor[x], {x, 0, 5}, 
     ExclusionsStyle -> {None, Black}]}, {Table[
     Plot[Sin[x], {x, 0, 2 Pi}, 
      Filling -> f], {f, {Axis, Top, Bottom, 0.3}}]}, {Plot[{Sin[x], 
      Cos[x]}, {x, 0, 2 Pi}, 
     Filling -> Axis]}, {Plot[{Sin[x], Cos[x]}, {x, 0, 2 Pi}, 
     Filling -> {1 -> Axis}]}, {Plot[{Sin[x], Cos[x]}, {x, 0, 2 Pi}, 
     Filling -> {1 -> {2}}]}, {Plot[{Sin[x], Cos[x]}, {x, 0, 2 Pi}, 
     Filling -> {1 -> {{2}, Yellow}}]}, {Plot[{Sin[x], Cos[x]}, {x, 0,
       2 Pi}, 
     Filling -> {1 -> {1/2, Yellow}}]}, {Plot[{Sin[x], Cos[x]}, {x, 0,
       2 Pi}, Filling -> {1 -> {{2}, {Yellow, Green}}}]}, {Table[
     Plot[Sin[x], {x, 0, 2 Pi}, Filling -> Axis, 
      FillingStyle -> c], {c, {Red, Green, Blue, 
       Yellow}}]}, {Plot[{Sin[x], Cos[x]}, {x, 0, 2 Pi}, 
     Filling -> Axis, 
     FillingStyle -> Directive[Opacity[0.5], Orange]]}, {Plot[
     Sin[x], {x, 0, 2 Pi}, Filling -> Axis, 
     FillingStyle -> {Red, Blue}]}, {Plot[Sin[x], {x, 0, 2 Pi}, 
     ColorFunction -> Function[{x, y}, Hue[y]], Filling -> Axis, 
     FillingStyle -> Automatic]}, {Plot[Sin[1/x], {x, 0.001, 0.1}, 
     Mesh -> All]}, {Table[ 
     Plot[Sin[1/x], {x, 0.001, 0.1}, MaxRecursion -> i, Mesh -> All, 
      Ticks -> None], {i, {0, 3, 6}}]}, {{Plot[Sin[x], {x, 0, 2 Pi}, 
      Mesh -> Full],
     Plot[Sin[x], {x, 0, 2 Pi}, Mesh -> All]}}, {Plot[
     Sin[x], {x, 0, 2 Pi}, Mesh -> 20]}, {Plot[Sin[x], {x, 0, 2 Pi}, 
     Mesh -> {Range[0, 2 Pi, Pi/4]}, 
     MeshStyle -> PointSize[Medium]]}, {Table[
     Plot[Tan[x], {x, 0, Pi/2}, MeshFunctions -> {f}, 
      Mesh -> 20], {f, {Function[{x, y}, x], 
       Function[{x, y}, y]}}]}, {Plot[Tan[x], {x, 0, Pi/2}, 
     Mesh -> {5, 10}, MeshFunctions -> {#1 &, #2 &}, 
     MeshStyle -> {Directive[PointSize[Medium], Red], Blue}]}, {Plot[
     Sin[x], {x, 0, 2 Pi}, Mesh -> 10, MeshFunctions -> {#1 &}, 
     MeshShading -> {Red, Blue}]}, {Plot[Sin[x], {x, 0, 2 Pi}, 
     Mesh -> 10, MeshFunctions -> {#1 &}, 
     MeshShading -> {Red, None}]}, {Plot[Sin[x], {x, 0, 2 Pi}, 
     Mesh -> 10, PlotStyle -> Thick, MeshFunctions -> {#1 &}, 
     MeshShading -> {Red, Blue}]}, {Plot[Sin[x], {x, 0, 2 Pi}, 
     Mesh -> 10, PlotStyle -> Green, MeshFunctions -> {#1 &}, 
     MeshShading -> {Red, Blue}]}, {Plot[Sin[x], {x, 0, 10}, 
     Mesh -> 10, PlotStyle -> Directive[Thick, Yellow], 
     MeshFunctions -> {#1 &}, 
     MeshShading -> {Red, Automatic}]}, {Plot[Sin[x], {x, 0, 10}, 
     Mesh -> 10, PlotStyle -> Thick, MeshFunctions -> {#1 &}, 
     MeshShading -> {Black, Automatic},
     ColorFunction -> Function[{x, y}, Hue[x]]]}, {Plot[
     Sin[x], {x, 0, 2 Pi}, Mesh -> 10, 
     MeshStyle -> Automatic]}, {Plot[Sin[x], {x, 0, 2 Pi}, Mesh -> 10,
      MeshStyle -> Red]}, {Plot[Sin[x], {x, 0, 2 Pi}, Mesh -> 10, 
     MeshStyle -> {Red, Blue}, MeshFunctions -> {#1 &, #2 &}]}, {Plot[
     Sin[x], {x, 0, 2 Pi}, Mesh -> 10, 
     MeshStyle -> Directive[PointSize[Large], Red]]}, {Timing[
     Plot[Sin[1/x], {x, 0, .01}, 
      PerformanceGoal -> "Quality"]]}, {Timing[
     Plot[Sin[1/x], {x, 0, .01}, PerformanceGoal -> "Speed"]]}, {Plot[
     Exp[x], {x, 0, 3}, 
     PlotLabel -> "exponential function"]}, {Plot[{Sin[x], 
      Cos[x]}, {x, 0, 2 \[Pi]}, 
     PlotLabels -> {"sine", "cosine"}]}, {Plot[{Sin[x], Cos[x]}, {x, 
      0, 2 \[Pi]}, PlotLabels -> Placed[{"sine", "cosine"}, Above]], 
    Plot[{Sin[x], Cos[x]}, {x, 0, 2 \[Pi]}, 
     PlotLabels -> {Placed["sine", Below], 
       Placed["cosine", Above]}]}, {Plot[{Sin[x], Cos[x]}, {x, 0, 
      2 \[Pi]}, 
     PlotLabels -> "Expressions"]}, {Plot[{Sin[x], Cos[x]}, {x, 0, 
      2 \[Pi]}, 
     PlotLabels -> {Callout["sin", {Scaled[0.25], Above}], 
       Callout["cos", {Scaled[0.5], Below}]}]}, {Plot[{Sin[x], 
      Cos[x]}, {x, 0, 2 \[Pi]}, 
     PlotLabels -> {"sine", None}]}, {Plot[{Sin[x], Cos[x]}, {x, 0, 
      10}]}, {Plot[{Sin[x], Cos[x]}, {x, 0, 10}, 
     PlotLegends -> "Expressions"]}, {Plot[{Sin[x], Cos[x]}, {x, 0, 
      10}, PlotLegends -> "Placeholder"]}, {Plot[{Sin[x], Cos[x]}, {x,
       0, 10}, 
     PlotLegends -> {"one", "two"}]}, {Plot[{Sin[x], Cos[x]}, {x, 0, 
      10}, PlotStyle -> {Red, Blue}, 
     PlotLegends -> "Placeholder"]}, {Plot[{Sin[x], Cos[x]}, {x, 0, 
      10}, PlotStyle -> {Red, Blue}, 
     PlotLegends -> Placed["Placeholder", Below]], 
    Plot[{x, Sqrt[x]}, {x, 0, 5}, PlotStyle -> {Red, Blue}, 
     PlotLegends -> 
      Placed["Expressions", {0.25, 0.75}]]}, {Plot[{Sin[x], 
      Cos[x]}, {x, 0, 10}, 
     PlotLegends -> 
      LineLegend["Expressions", LegendFunction -> Frame]]}, {Table[
     Plot[Sin[x], {x, 0, 2 Pi}, PlotPoints -> i, 
      MaxRecursion -> 0], {i, {5, 10, 15, 25}}]}, {Plot[
     Sqrt[x], {x, -5, 5}, PlotRange -> Full]}, {Plot[
     Sqrt[x], {x, -5, 5}, PlotRange -> Automatic]}, {Plot[
     Sqrt[x], {x, -5, 5}, PlotRange -> 2]}, {Plot[1/x, {x, -2, 2}, 
     Frame -> True]}, {Plot[1/x, {x, -2, 2}, Frame -> True, 
     PlotRangeClipping -> False]}, {Table[
     Plot[Sin[x], {x, 0, 2 Pi}, 
      PlotStyle -> ps], {ps, {Red, Thick, Dashed, 
       Directive[Red, Thick]}}]}, {Plot[{Sin[x], Sin[2 x], 
      Sin[3 x]}, {x, 0, 2 Pi}]}, {Plot[{Sin[x], Sin[2 x], 
      Sin[3 x]}, {x, 0, 2 Pi}, 
     PlotStyle -> {Red, Green, Blue}]}, {Plot[Sin[x], {x, 0, 2 Pi}, 
     PlotStyle -> Thick, 
     ColorFunction -> Function[{x, y}, Hue[y]]]}, {Plot[
     Sin[x], {x, 0, 2 Pi}, 
     PlotStyle -> Directive[Opacity[0.5], Thick], Mesh -> 10, 
     MeshFunctions -> {#1 &}, MeshShading -> {Red, Blue}]}, {Plot[
     Sin[x], {x, 0, 2 Pi}, PlotStyle -> Red, 
     Mesh -> All]}, {Plot[{Sin[x], Cos[x]}, {x, 0, 2 Pi}, 
     PlotTheme -> "Business"]}, {Plot[{Sin[x], Cos[x]}, {x, 0, 2 Pi}, 
     PlotTheme -> "Business", PlotStyle -> 96]}, {Plot[
     Sin[x], {x, 0, 8 Pi}, 
     RegionFunction -> 
      Function[{x, y}, Pi/2 < Mod[x, 2 Pi] < 3 Pi/2]]}, {Plot[
     Sin[x], {x, 0, 8 Pi}, 
     RegionFunction -> Function[{x, y}, Abs[y] > 0.5]]}, {Plot[
     x^2, {x, 0, 10}]}, {Plot[x^2, {x, 0, 10}, 
     ScalingFunctions -> "Log"]}, {Plot[x^2, {x, 0, 10}, 
     ScalingFunctions -> "Reverse"]}, {Plot[x^2, {x, 1, 10}, 
     ScalingFunctions -> "Reciprocal"]}, {Plot[x^2, {x, 0, 10}, 
     ScalingFunctions -> {"Reverse", "Log"}]}, {Plot[x^2, {x, 0, 10}, 
     ScalingFunctions -> {"Reverse", None}]}, {Plot[x^2, {x, 0, 10}, 
     ScalingFunctions -> {None, {-Log[#] &, Exp[-#] &}}]}, {Plot[
     x^2, {x, 1, 10}, ScalingFunctions -> "Log", 
     Ticks -> {Automatic, 2^Range[10]}, 
     GridLines -> {None, 2^Range[10]}]}, {Plot[x^2, {x, 1, 10}, 
     ScalingFunctions -> "Log", PlotRange -> {1, 100}, 
     AxesOrigin -> {Automatic, 10}]}, {Plot[
     Sin[x + 10^20], {x, 0, 2 Pi}, 
     WorkingPrecision -> MachinePrecision]}, {Plot[
     Sin[x + 10^20], {x, 0, 2 Pi}, WorkingPrecision -> 20]}}, 
 "Applications" -> {{Plot[{x^(1/2), x, x^2}, {x, 0, 2}, 
     PlotLegends -> "Expressions"]}, {Plot[{Exp[x], Log[x], 
      x}, {x, -3, 3}, PlotRange -> 3, 
     PlotStyle -> {Red, Green, Dashed}, 
     AspectRatio -> Automatic]}, {Plot[{x Sin[1/x], 
      Abs[x], -Abs[x]}, {x, -1/2, 1/2}, 
     PlotStyle -> {Red, Directive[Dashed, Gray], 
       Directive[Dashed, Gray]}]}, {Plot[Tan[x], {x, -5, 5}], 
    Plot[Tan[x], {x, -5, 5}, ExclusionsStyle -> Dashed]}, {Plot[
     Sin[Floor[x]], {x, 0, 10}, ExclusionsStyle -> Dotted], 
    Plot[Sin[Floor[x]], {x, 0, 10}, Exclusions -> {Sin[\[Pi] x] == 0},
      ExclusionsStyle -> Dashed]}, {Plot[
     Sin[Sqrt[2] x] + Sin[x], {x, 0, 20}], 
    Plot[Sin[Sqrt[2] x] + Sin[x], {x, 0, 20}, 
     MeshFunctions -> {Function[{x, y}, y]}, Mesh -> {{0}}, 
     MeshStyle -> Directive[PointSize[Medium], Red]]}, {Plot[
     Sin[Sqrt[2] x] + Sin[x], {x, 0, 50}], 
    mf = Function[{x, y}, Evaluate@D[Sin[Sqrt[2] x] + Sin[x], x]];, 
    Plot[Sin[Sqrt[2] x] + Sin[x], {x, 0, 50}, MeshFunctions -> {mf}, 
     Mesh -> {{0}}, 
     MeshStyle -> Directive[PointSize[Medium], Red]]}, {f = 
      Sin[Sqrt[2] x] + Sin[x];, Plot[f, {x, 0, 50}], 
    Plot[f, {x, 0, 50}, 
     Exclusions -> {{D[f, x] == 0, D[f, {x, 2}] <= 0}}, 
     ExclusionsStyle -> Directive[Thickness[0.02], Red]], 
    Plot[f, {x, 0, 50}, 
     Exclusions -> {{D[f, x] == 0, D[f, {x, 2}] >= 0}}, 
     ExclusionsStyle -> Directive[Thickness[0.02], Purple]]}, {f = 
      Sin[Sqrt[2] x] + Sin[x];, Plot[f, {x, 0, 50}], 
    Plot[f, {x, 0, 50}, Filling -> {{1 -> {0, {Red, Blue}}}}, 
     PlotLegends -> 
      SwatchLegend[{Blue, Red}, {"non-negative", 
        "non-positive"}]]}, {f = Sin[Sqrt[2] x] + Sin[x];, 
    plot = Plot[f, {x, 0, 50}], 
    rfi = Function[{x, y}, Evaluate[D[f, x] >= 0]];, 
    incr = Plot[f, {x, 0, 50}, RegionFunction -> rfi, 
      PlotStyle -> Blue], 
    rfd = Function[{x, y}, Evaluate[D[f, x] <= 0]];, 
    decr = Plot[f, {x, 0, 50}, RegionFunction -> rfd, 
      PlotStyle -> Red], 
    Legended[Show[incr, decr], 
     SwatchLegend[{Blue, Red}, {"increasing", "decreasing"}]]}, {f = 
      Sin[Sqrt[2] x] + Sin[x];, plot = Plot[f, {x, 0, 50}], 
    rfcvx = Function[{x, y}, Evaluate[D[f, {x, 2}] >= 0]];, 
    cvx = Plot[f, {x, 0, 50}, RegionFunction -> rfcvx, 
      PlotStyle -> Orange], 
    rfccv = Function[{x, y}, Evaluate[D[f, {x, 2}] <= 0]];, 
    ccv = Plot[f, {x, 0, 50}, RegionFunction -> rfccv, 
      PlotStyle -> Blue], 
    Legended[Show[cvx, ccv], 
     SwatchLegend[{Orange, Blue}, {"convex", "concave"}]]}, {f = 
      Sin[Sqrt[2] x] + Sin[x];, 
    Plot[f, {x, 0, 
      20}], {min, max} = {NMinValue[{D[f, x], 0 <= x <= 20}, x], 
       NMaxValue[{D[f, x], 0 <= x <= 20}, x]};, 
    df = Rescale[D[f, x], {min, max}, {0, 1}], Plot[df, {x, 0, 20}], 
    cf = Function[{x}, Evaluate[ColorData["Rainbow"][ df]]], 
    leg = BarLegend[{ColorData["Rainbow"][
          Rescale[#, {min, max}, {0, 1}]] &, {min, max}}, 
       LegendMarkerSize -> 150];, 
    Plot[f, {x, 0, 20}, ColorFunction -> cf, 
     ColorFunctionScaling -> False, PlotLegends -> leg], 
    Plot[f, {x, 0, 20}, ColorFunction -> cf, 
     ColorFunctionScaling -> False, Filling -> 0, 
     PlotLegends -> leg]}, {Plot[{Re[Exp[I \[Omega]]], 
      Im[Exp[I \[Omega]]]}, {\[Omega], 0, 10}, 
     PlotLegends -> 
      "Expressions"]}, {Plot[{Abs[Exp[I \[Omega]]/(1 + \[Omega]^2)], 
      Arg[Exp[I \[Omega]]/(1 + \[Omega]^2)]}, {\[Omega], -\[Pi], \
\[Pi]}, PlotLegends -> "Expressions"]}, {f = 
      Exp[I \[Omega]]/(1 + \[Omega]^2);
    cf = Function[\[Omega], Evaluate[Hue[Arg[f]/(2 \[Pi]), 0.5]]], 
    Plot[Abs[f], {\[Omega], -\[Pi], \[Pi]}, ColorFunction -> cf, 
     ColorFunctionScaling -> False], 
    Plot[Abs[f], {\[Omega], -\[Pi], \[Pi]}, ColorFunction -> cf, 
     ColorFunctionScaling -> False, Filling -> Bottom, 
     PlotLegends -> 
      BarLegend[{cf, {-\[Pi], \[Pi]}}, 
       LegendMarkerSize -> 150]]}, {s = 
     DSolve[y'[x] == 1/(1 + y[x]), y, x], 
    Plot[Evaluate[y[x] /. s /. C[1] -> 0], {x, -2, 5}], 
    Plot[Evaluate[y[x] /. s /. C[1] -> Range[0, 5]], {x, -5, 
      5}]}, {s = Reduce[Sin[x^2 + y] == 0, {x, y}], 
    Plot[Evaluate[{-x^2 + 2 \[Pi] C[1], \[Pi] - x^2 + 
         2 \[Pi] C[1]} /. C[1] -> Range[-5, 5]], {x, -5, 5}]}}, 
 "PropertiesRelations" -> {{Plot[Sin[x], {x, 0, 10}, 
     Mesh -> All]}, {{Plot[Sin[x^2], {x, 0, 5}], 
     ParametricPlot[{x, Sin[x^2]}, {x, 0, 5}, 
      AspectRatio -> 
       1/GoldenRatio]}}, {{ParametricPlot[{Cos[\[Theta]], 
       Sin[\[Theta]]}, {\[Theta], 0, 2 Pi}], 
     ParametricPlot[{r Cos[\[Theta]], r Sin[\[Theta]]}, {\[Theta], 0, 
       2 Pi}, {r, 1, 2}]}}, {{ContourPlot[
      x^2 + y^2 == 1, {x, -1, 1}, {y, -1, 1}], 
     RegionPlot[
      1 < x^2 + y^2 < 4, {x, -2, 2}, {y, -2, 2}]}}, {LogLogPlot[
     Abs[10^2/((I \[Omega])^2 + 100)], {\[Omega], 10^0, 
      10^5}]}, {{ListLinePlot[Table[{x, Sin[x]}, {x, 0, 10, 0.25}]], 
     Plot[Sin[x], {x, 0, 
       10}]}}, {Plot3D[(x^2 + y^2) Exp[-(x^2 + y^2)], {x, -2, 
      2}, {y, -2, 2}], 
    ParametricPlot3D[{-2 Cos[u] Cos[v]^3, -2 Cos[v]^2 Sin[u], 
      2 Tan[v]}, {u, 0, 2 Pi}, {v, -1, 1}]}}, "PossibleIssues" -> {}, 
 "InteractiveExamples" -> {}, 
 "NeatExamples" -> {{f[n_, x_] := 
     Abs[((1/Pi)^(1/4) HermiteH[n, x])/(E^(x^2/2) Sqrt[2^n n!])]^2, 
    Plot[Evaluate@
        Append[Table[f[n, x] + n + 1/2, {n, 0, 7}], x^2/2], {x, -4, 
      4}, Filling -> Table[n -> n - 1/2, {n, 1, 8}]]}}}