Use lagrange multipliers to find the shortest distance

  • Thread starter anubis01
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  • #1
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Homework Statement


Use lagrange multipliers to find the shortest distance between a point on the elliptic paraboloid z=x^2 +y^2


Homework Equations





The Attempt at a Solution


http://img716.imageshack.us/img716/7272/cci1902201000000.jpg [Broken]

I'm not that good with using the equation editor, so I scanned my work.

I'm stuck on the last part where i'm trying to factor the equation to find a solution for [tex]\lambda[/tex], I cant seem to find a solution that would make the equation zero, which is what i need in order to do the long division to factor that equation.
 
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Answers and Replies

  • #2
Dick
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Your constraint is x^2+y^2-z=0. You differentiate lambda*(x^2+y^2-z). So you have a mistake on step 3. The d/dz equation should be 2*(z-1/2)=(-lambda). That may be why you are having a hard time with the resulting equation.
 
  • #3
149
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ah, now the equation makes much more sense, thanks for the help.
 

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