Re: visualizing a maximum in the intersection between

*To*: mathgroup at smc.vnet.net*Subject*: [mg131096] Re: visualizing a maximum in the intersection between*From*: leigh pascoe <leigh at evry.inserm.fr>*Date*: Tue, 11 Jun 2013 02:30:51 -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>

Le 08/06/2013 08:34, dusko.cakara at gmail.com a =C3=A9crit : > 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