plotting - Show shows two objects separated by a comma instead one on top of another

As in the title. I want them to be on the same graph. Additionaly i want to the graph to always be focused on the rectangle.

f[x_, x0_, a_, n0_, C_] := -1/a + C/(a*n0)*Cosh[a*n0/C*(x - x0)]

Show[
  Graphics[{Thick, Opacity[0.5], LightBlue, Rectangle[{0, -1}, {3, 1}]}]

  Manipulate[
    Plot[f[x, x0, a, n0, c], 
    {x, 0, 3}], 
    {x0, 0, 10}, 
    {a, -1, 1}, 
    {n0, 1, 2}, 
    {c, 0.1, 10}]]

Second question, I don't know if i should make another thread about it. How to add two points where the rectangle and function collide?

Answer

You can also use the rectangle as a Prolog or Epilog in Plot so that you don't have to use Show.

The intersection of the rectangle with the plotted line can be highlighted using Mesh* options:

Manipulate[Plot[f[x, x0, a, n0, c], {x, 0, 3}, 
  PlotRange -> {{-1, 4}, {-2, 4}}Frame -> True, Axes -> False, 
  MeshStyle -> Directive[Green, PointSize[Large]], 
  MeshFunctions -> {#2 &}, Mesh -> {{1, -1}}, 
  MeshShading -> {Blue, Red}, BaseStyle -> Thick, 
  Prolog -> {EdgeForm[{LightBlue, Thick}], Opacity[0.5], LightBlue, 
    Rectangle[{0, -1}, {3, 1}]}], 
 {{x0, 1.5}, 0, 10}, {{a, -.3}, -1, 1}, {{n0, 1.1}, 1, 2}, {{c, 0.1}, 0.1, 10}]

Comments

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calculus and analysis - Integral of the Sinc product

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