       Re: visualizing a maximum in the intersection between two surfaces

• To: mathgroup at smc.vnet.net
• Subject: [mg131080] Re: visualizing a maximum in the intersection between two surfaces
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Mon, 10 Jun 2013 04:10:43 -0400 (EDT)
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• References: <20130608063415.570076A22@smc.vnet.net>

```An alternate method

Show[
ContourPlot3D[Tooltip[x + y == 1],
{x, 0, 1}, {y, 0, 1}, {z, 0, 1/2},
ContourStyle -> Opacity[.7],
MeshStyle -> Gray],
Plot3D[Tooltip[x*y], {x, 0, 1}, {y, 0, 1},
PlotStyle -> Opacity[.7],
Exclusions -> {x == 1/2, y == 1/2, x + y == 1},
ExclusionsStyle ->
Directive[Opacity, Black, Thick],
MeshStyle -> Gray,
PlotPoints -> 100]]

Bob Hanlon

On Sat, Jun 8, 2013 at 2:34 AM, <dusko.cakara at gmail.com> wrote:

> Hello,
> 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?
>