plotting - Marking points of intersection between two curves

I'm trying to illustrate the solutions numerically and graphically for an equation such as Tan[x] == x. I think I did everything ok except I wanted to mark each intersection between Tan[x] and x.

Does anyone know how such a thing can be done?

Answer

Edited to make it a function. For the strange Exclusions specification I use below, see my answer here. Thanks to @Oleksandr and @JM for their great comments.

plInters[{f1_, f2_}, {min_, max_}] :=
 Module[{sol, x},
         sol = x /. NSolve[f1[x] == f2[x] && min < x < max, x];
         Framed@Show[
                  ListPlot[{#, f1[#]} & /@ sol, PlotStyle -> PointSize[Large]],
                  Plot[{f1[x], f2[x]}, {x, min, max}, Exclusions -> {True, f2[x] == 10, f1[x] == 10}]

    ]
  ]


GraphicsRow[plInters[#, {-10, 10}] & /@ {{# &, Tan}, {Tan, Coth}, {Sin, 1/# &}}]

Mathematica graphics

Comments

plotting - Plot 4D data with color as 4th dimension

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plotting - Filling between two spheres in SphericalPlot3D

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plotting - Mathematica: 3D plot based on combined 2D graphs

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