MathGroup Archive 2007

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

Search the Archive

Re: Is this a problem in mathematica?


On Mar 28, 2007, at 2:44 AM, traz wrote:

> Let's say I wanna solve this problem:
>
> Determine point(s) on y = x^2 +1 that are
> closest to (0,2).
>
> So in mathematica:
>
> minDist = (x - 0)^2 + (y - 2)^2;
> Minimize[minDist, y == 1 + x^2, {x, y}]
>
> Output will give you: x -> -1/Sqrt[2], y -> 3/2
>
> but x also has another answer: +1/Sqrt[2]. Is this a problem in  
> mathematica or can my code be changed to output the other value of  
> x for the minimum distance?

Minimize just searches for a minimum, if there are two or more minima  
it will only find one at most.  If you want general solutions use  
Solve to find the minima of the first derivative.

In[4]:=
Solve[D[x\^2 + (1 + x^2 - 2)^2, x]== 0, x]
Out[4]=
{{x -> 0}, {x -> -1/Sqrt[2]}, {x -> 1/Sqrt[2]}}

Checking the distance for each point will allow you to reject the  
point at 0 as a minimum.

Regards,

Ssezi


  • Prev by Date: Closing All Input Cells at Once
  • Next by Date: Re: Multi-core Support in Mathematica 5.2
  • Previous by thread: Is this a problem in mathematica?
  • Next by thread: Re: Is this a problem in mathematica?