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LeGrange Multipliers Finding critical points of function

  1. Oct 15, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the critical points of [itex]f(x,y)=x+y^2[/itex] subject to the constraint [itex]g(x)=x^2+y^2=1[/itex]



    2. Relevant equations
    [itex]\nabla f=\lambda\nabla g[/itex]
    [itex]g(x,y)=1[/itex]



    3. The attempt at a solution

    [tex]f_x=1=2\lambda*x\Rightarrow x=\frac{1}{2\lambda}[/tex]

    [tex]f_y=2y=2\lambda*y\Rightarrow y(\lambda-1)=0\Rightarrow y=0 \\ or\\ \lambda=1[/tex]

    [tex]x^2+y^2=1[/tex]

    I am a little confused as to where I go from here?
     
  2. jcsd
  3. Oct 16, 2008 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    You've done the hard part. If y= 0, then [itex]\lambda[/itex] doesn't matter: Find x from x2+ y2= 1. If [itex]\lambda= 1[/itex], then x= 1/2 and you can find y from x2+ y2= 1.
     
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