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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

    dz/dx=6x

    dx/dy=-2y

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

    Then using the above relation I solved for each variable getting
    1.y=√(9-x2)

    2.x=√(1-1/9y2)

    We already have the relation from the partials

    A.-2y=0

    B.6x=0
    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

    haruspex

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    ∂z/∂y
    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?

    RGV
     
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