Re: visualizing a maximum in the intersection between two surfaces

*To*: mathgroup at smc.vnet.net*Subject*: [mg131101] Re: visualizing a maximum in the intersection between two surfaces*From*: Dusko Cakara <dusko.cakara at gmail.com>*Date*: Tue, 11 Jun 2013 02:32:31 -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>

Thanks Leigh, Thank you! Of course this simple graph is obtained after solving the problem analytically (solving the set of eqs). However the point that I must outline to my students is that the condition x+y=1 actually reduces the dimensionality of x*y, and I think the best way is visualizing the projection of the x+y=1 line onto the z=x*y surface in [x,y,z]. Best regards Dusko On Mon, Jun 10, 2013 at 11:22 AM, leigh pascoe <leigh at evry.inserm.fr> wrote: > Le 08/06/2013 08:34, dusko.cakara at gmail.com a =E9crit : > > 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 > > > > > Here is one easy way. > > Plot[x*(1 - x), {x, 0, 1}] > > This gives a plot of all the points x*y satisfying the condition x+y=1 > (or y=(x-1)). The maximum of .25 occurs when x=y=1-x > > Leigh >

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