Dynamic tangential plane - how?

*To*: mathgroup at smc.vnet.net*Subject*: [mg92909] Dynamic tangential plane - how?*From*: "m.g." <mg at michaelgamer.de>*Date*: Sat, 18 Oct 2008 06:24:40 -0400 (EDT)

Hello Group, I=B4m trying to visualize the tangential plane to a function f(x,y). I =B4ve done various attemps - none of them was successfull. Here an extract of my attempts: f[x_, y_] := (1 - x^2) (2 x - y^3) grad[x_, y_] := {2 (1 - x^2) - 2 x (2 x - y^3), -3 (1 - x^2) y^2} DynamicModule[{a = 1, b = 1, p, q, punkt}, {Slider2D[Dynamic[{a, b}], {{-2, -2}, {2, 2}}], p = Plot3D[f[x, y], {x, -2, 2}, {y, -2, 2}], punkt = Dynamic @ Graphics3D[{PointSize[Large], Red, Point[{a, b, f[a, b]}]}], q = Dynamic @ Plot3D[f[a, b] + grad[a, b].{x - a, y - b}, {x, -2, 2}, {y, -2, 2}] } ] Here the three parts I need (the surface of f, the tangential plane and the point "punkt" where the plane touches the surface) are shown, side by side.How can I manage it, that this three graphics are put together in ONE Graphics. The attempt DynamicModule[{a = 1, b = 1, p, q, punkt}, {Slider2D[Dynamic[{a, b}], {{-2, -2}, {2, 2}}], punkt = Dynamic @ Graphics3D[{PointSize[Large], Red, Point[{a, b, f[a, b]}]}], q = Dynamic @ Plot3D[{f[x, y], f[a, b] + grad[a, b].{x - a, y - b}}, {x, -2, 2}, {y, -2, 2}] } ] Changes f[x,y] (!!!), but only a and b are dynamically changing. How could this happen?? Any hints appreciated. Greeting from Germany Mike