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Plot[{Tan[x], x Sin[x]}, {x, -8, 8}, MeshFunctions -> {Tan[#] - # 
Sin[#] &}, Mesh -> {{0.0}}, MeshStyle -> Directive[Red, 
PointSize[Large]]]

Just as the picture shows, there are some incorrect points around the intersection point.

I want to put a red point on the lines' intersection, but it does't work.

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1 Answer 1

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When using MeshFunctions, it is often a good idea to reformulate your functions so that it is free of poles or other singularities:

Plot[{Tan[x], x Sin[x]}, {x, -8, 8}, 
     MeshFunctions -> {Sin[#] - # Sin[2 #]/2 &}, Mesh -> {{0}}, 
     MeshStyle -> Directive[Red, PointSize[Large]]]

intersections

Similar principles apply to the use of e.g. FindRoot[] for finding intersections.

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