MathGroup Archive 2013

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: visualizing a maximum in the intersection between two surfaces


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
>


  • Prev by Date: Re: visualizing a maximum in the intersection between two surfaces
  • Next by Date: Re: Not sure this limit is right...
  • Previous by thread: Re: visualizing a maximum in the intersection between two surfaces
  • Next by thread: Re: mma.el -- emacs mode for writing mathematica package files