Re: visualizing a maximum in the intersection between two surfaces

*To*: mathgroup at smc.vnet.net*Subject*: [mg131072] Re: visualizing a maximum in the intersection between two surfaces*From*: Bob Hanlon <hanlonr357 at gmail.com>*Date*: Sun, 9 Jun 2013 04:31:29 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net*References*: <20130608063415.570076A22@smc.vnet.net>

ParametricPlot3D[ {x, 1 - x, x (1 - x)}, {x, 0, 1}, Exclusions -> {x == 0.5}, ExclusionsStyle -> Directive[Red, AbsoluteThickness[5]], AxesLabel -> (Style[#, 14, Bold] & /@ {"x", "y", "x y"})] Manipulate[ Column[{ ParametricPlot3D[ {x, 1 - x, x (1 - x)}, {x, 0, 1}, Exclusions -> {x == xv}, ExclusionsStyle -> Directive[Red, AbsoluteThickness[5]], AxesLabel -> (Style[#, 14, Bold] & /@ {"x", " y", "x y "}), ImageSize -> 400], , StringForm[ "x = ``, y = ``, z = x y = ``", Round[xv, 1/100] // N, Round[1 - xv, 1/100] // N, Round[xv (1 - xv), 1/1000] // N]}], {{xv, .5, "x"}, 0, 1, 0.01, Appearance -> "Labeled"}] Bob Hanlon On Sat, Jun 8, 2013 at 2:34 AM, <dusko.cakara at gmail.com> wrote: > Hello, > can somebody please help: > I want to visualize that for x+y=1, maximum x*y occurs when y=0.5 and > x=0.5. > > Graphically, this can be visualized as the maximum of the projection curve > of the x+y=1 line in the x-y plane, at the x*y surface. Equivalently, we > can look for the maximum in the intersection curve between the surface x*y > and the surface peripendicular to the x-y plane with the base x+y=1. > > Can I plot this in a simple manner? > > Thanks in advance! > Dusko > >

**References**:**visualizing a maximum in the intersection between two surfaces***From:*dusko.cakara@gmail.com