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# Show the high of the levels in ContourPlot?

Posted 5 years ago
 I have looked up in the Mathematica Documention Center the answerfor my problem but unfortunatteny they make available only a few examples and details. My problem is to plot a contour of the function f(x,y)= Exp[-y^2 - x^4/4 + x^2], indicating the height of each level and putting a point (or a cross) on the two local maximum at (-2^(1/2),0) and at (2^(1/2),0)( which is "e") .Besides these I would like to color the zero level differenttily of the others. thank you. Ana Luiza Plot3D[Exp[-y^2 - x^4/4 + x^2], {x, -2.5, 2.5}, {y, -2.5, 2.5}] ContourPlot[ f[x, y] == {0.5, 0.7, 1.5, 2.0, 2.71}, {x, -2.5, 2.5}, {y, -2.5, 2.5}] 
 Hello Ana Luiza, first, locate the maxima: f[x_, y_] := Exp[-y^2 - x^4/4 + x^2]; Plot3D[f[x, y], {x, -2.5, 2.5}, {y, -2.5, 2.5}] Zone = Polygon[{{-2.5, -2.5}, {-2.5, 2.5}, {2.5, 2.5}, {2.5, -2.5}}]; Sup1 = ArgMax[f[x, y], {x, y} \[Element] Zone]; Sup2 = {x, y} /. Last@FindMaximum[f[x, y], {x, -1}, {y, 0}]; (AgMax finds a single max).Then plot Show[ContourPlot[f[x, y], {x, -2.5, 2.5}, {y, -2.5, 2.5}, Contours -> {0.5, 0.7, 1.5, 2.0, 2.71}, ContourLabels -> True], Graphics[{Green, PointSize[Large], Point[Sup1]}] , Graphics[{Red, PointSize[Large], Point[Sup2]}]]