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Finding absolute extrema with only 1 critical point

  1. Mar 12, 2013 #1
    1. The problem statement, all variables and given/known data
    Edit: Not absolute, just extrema

    I've already found the critical point to be (-1/2, -1/4, 1/2) with a value of -1/2. My only problem is finding whether this is a max or min. What technique do I use to find out? I don't believe I can use the 2nd derivative test because all the 2nd partial derivatives will equal 0.


    f(x,y,z) = x + 2y + z

    constraint => x^2 + 4y^2- z = 0


    2. Relevant equations



    3. The attempt at a solution

    Critical point (-1/2, -1/4, 1/2). Value = -1/2

    How do I determine whether that is a max or min?
     
    Last edited: Mar 12, 2013
  2. jcsd
  3. Mar 12, 2013 #2

    Dick

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    Science Advisor
    Homework Helper

    Assuming you did everything right the best first method is just to think about it. x=0, y=0, z=0 also satisfies your contraint. So?
     
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