ploting "contour plot" and "2D plot"



> > 
> > http://commons.wikimedia.org/wiki/File:LagrangeMultipliers3D.png


Maybe something like this can help:

load(draw);

/* bell-shaped surface */
f(x, y) := 20*exp(-x^2-y^2)-10;

/* these is how y depends on x in the plane
   2*x - y + 1 = 0, parallel to OZ axis */
y(x) := 2*x+1;

draw3d(
    /* bell */
    color = green,
    explicit(f(x,y),x,-2,2,y,-3,3),
    contour_levels = 15,   /* you can select contours */
    contour        = both, /* and where to draw them */

    /* interseccion curve between bell and plane */
    color = blue,
    line_width = 3,
    parametric(t, y(t), f(t, y(t)), t, -2,1) ) ;

for help, type

? contour
? contour_levels



As Jaime said, you need some hand work to compose the scene.

--
Mario