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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)
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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
>
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