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Topic: visualizing a maximum in the intersection between two surfaces
Replies: 6   Last Post: Jun 11, 2013 2:25 AM

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 leigh pascoe Posts: 30 Registered: 3/2/10
Re: visualizing a maximum in the intersection between
Posted: Jun 11, 2013 2:24 AM

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

Date Subject Author
6/9/13 Bob Hanlon
6/10/13 Bob Hanlon
6/11/13 dusko.cakara@gmail.com
6/11/13 leigh pascoe
6/11/13 dusko.cakara@gmail.com
6/11/13 dusko.cakara@gmail.com