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Homework Help: Directional derivatives and gradients

  1. Nov 6, 2012 #1
    1. The problem statement, all variables and given/known data[/b]
    Let z=3x2-y2. Find all points at which magnitude(nabla Z)=6

    First things first

    I took the partials dz/dx and dz/dy



    I know that √(36x2+4y2)=6 or (36x2+4y2)=36

    Then using the above relation I solved for each variable getting


    We already have the relation from the partials


    So I plugged in 1 into A and 2 into B to get the following

    x=+-1 and y=+-3

    However the answers don't check out

    Where did I go wrong?
  2. jcsd
  3. Nov 6, 2012 #2


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    No - try that again.
  4. Nov 6, 2012 #3

    Ray Vickson

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    Why do you try to set dz/dx = 0, and/or dz/dy = 0?

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