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The Documentation Center article on Plot notes under Details and Options that Method is one of the options for Plot.

However, it doesn't mention what Method values are allowed, and neither does the article on Method.

The Options section of the Plot article gives details on 91 options, but Method isn't one of them.

The more general problem I'm having: when I do Plot[f[x], {x, a, b}] for a certain function, Plot graphs it just fine, but spews out a ton of warnings that suggest Plot is trying to symbolically differentiate (or otherwise symbolically manipulate) my function, which is impossible since f is defined with SetDelayed.

To avoid these warnings, I want to tell Plot to only evaluate this function numerically and not attempt to find its derivative/etc.

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Below are a bunch, although they seem to be a compilation of options for many or all plotting functions, including (mainly) 3D functions. As @belisarius remarked in a comment, using ?NumericQ is the standard way to prevent symbolic analysis, if indeed Plot is doing such. Use something like

nf[x_?NumericQ] := f[x];
Plot[f[x], {x, a, b}]

Without a specific f[x] that reproduces the problem, it is impossible to check whether a particular "fix" will in fact work or even if the function is being differentiated. (3D plots often compute normals, but I have never noticed that any 2D plots that compute derivatives.)

*Plot* method options:

Charting`CommonDump`$VisualizationMethodOptions

(*   {"ScalingFunctions", "PlotRandomSeed", "DraftRendering", "ArrayPlot", 
"InvertNormalsDirection", "BoundaryOffset", "Refinement", 
"MeshBoundaryValues", "StepsJoined", "SurfaceStitch", 
"UnboundedPolygons", "InterpolateMesh", "DownsampleWindow", 
"FilterMeshAll", "OriginalCoordinates", "ReturnMeshObject", 
"ReturnRawMeshObject", "MeshMaxRecursion", "ContourMaxRecursion", 
"DelaunayDomainScaling", "PolygonReverse", "VertexAliasTolerance", 
"Average", "Fan", "Seidel", "Constrained", "GradientAligned", 
"MeshRegions", "PathPolygons", "SimplifyPaths", 
"PackGraphicsComplex", "SnapContourVertex", "PlotTheme", 
"VertexColorsPalette", "VectorBackgroundPadding", "ReturnImage", 
"Closed3DRegion", "PolygonColoring", "Equalized", "EqualizeColor", 
"ColorFunctionData", "Valence", "Laplace", "Conformal", 
"RGBColorSpace", "GrayColorSpace", "ParallelPlotEvaluate", 
"ParallelPlotMethod", "ParallelPlotParameters", "LightingMethod", 
"DiffuseReflection", "AspectBasedShading", "Contrast", "Brightness", 
"Saturation", "SpatialResolution", "ElevationDefault", 
"IlluminationModel", "AngularDistanceRadius", "UseNumericalFunction", 
"NumericalFunction", "FlattenFunctions", "SuppressMessages", 
"MessagesHead", "MappingFunctions", "DomainMappingFunctions", 
"LegacyColorFunctionProcessing", "ContourShadingPrefixFunction", 
"ContoursPrefixFunction", "UseCaching", "CutMeshLines", 
"FillBoundaryLines", "Ungroup", "CloseMeshThickness", 
"ClipNoneMeshShading", "ClipAtPlotRange", "ClipMeshOverlay", 
"ClipBoundaryLines", "Subdivision", "CellDecomposition", "Divisions", 
"ControlValue", "VertexTolerance", "MaxBoundaryEdgeLength", 
"CellCuboids", "Dihedral", "Gaussian", "GradientNorm", "Loop", 
"Contouring", "Curvature", "ContourLevel", "PlanarRectangular", 
"Triangular", "Quad", "QuadTriangular", "Length", "Area", 
"Perimeter", "BhatiaLawrence", "AverageNormal", "WeightedNormal", 
"Barycenter", "Cotangents", "Circumcenter", "Incenter", "Inradius", 
"Circumradius", "InteriorAngles", "Dual", "OFF", "NOFF", "Frenet", 
"NaturalNeighbour", "InverseDistance", "Kriging", "MaxMemoryUse", 
"Intersect", "FullLattice", "MarchingCubes", "AdvancedMarchingCubes", 
"AdaptiveTriangular", "Octree", "OctreeCubes", "Algebraic", 
"Cubical", "Tetra", "Seeds", "Linear", "Bisect", "NoiseDelta", 
"ContourSpacing", "MeshSpacing", "Quantile", "CurveLength", 
"ArcLength", "DataLineMesh", "DataPointMesh", "GraphicsIndex", 
"SymbolicPiecewiseSubdivision", "pw", "PiecewiseTimeConstraint", 
"SymbolicPointsTimeConstraint", "Singularities", "Isolated", 
"SingularCurves", "SingularMaxRecursion", "ExclusionsOffset", 
"PolygonReduction", "Polygons", "PolygonContraction", 
"PointPlacement", "QuadricWeighting", "CompactnessRatio", 
"MeshPenalty", "BoundaryWeight", "EndPoint", "EndOrMidPoint", 
"LinearPoint", "OptimalPoint", "UniformWeight", "AreaWeight", 
"AngleWeight", "AverageWeight", "AreaAverageWeight", "NormalWeight", 
"VerticesGoal", "EdgesDistanceGoal", "MinArea", 
"PreserveInteriorFaces", "SegmentPartition", "SegmentLengthGoal", 
"LegendsFunction", "Legend", "Extrapolation", "Interpolation", 
"PointsToSpheres", "Caps", "ConnectEnds", "StreamlinesMethod", 
"StreamlinesSamplingStep", "StreamlinesInsertionStep", 
"StreamlinesParameterLimit", "StreamlinesNDSolve", 
"StreamlinesNumericalFunction", "LICLines", "LICMinHits", 
"LICMaxLines", "AccuracyGoal", "PrecisionGoal", "HSBChannel", 
"LICModulate", "NewtonFlow", "PerturbateFrame", "PerturbateSeeds", 
"ParseGlyphStyle", "LinePath", "LineArrow", "GlyphPath", 
"Directional", "DirectionalScaled", "Velocity", "VelocityScaled", 
"ControlPoints", "BSplineCurve", "BezierCurve", "NURBSCurve", 
"XSplineCurve", "BSplineShape", "BezierShape", "NURBSShape", 
"XSplineShape", "SharedMemoryReference", "Method", "Automatic", 
"None", "All", "True", "False"}   *)
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