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Maximum pointed devertive

  1. Sep 13, 2004 #1

    ori

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    the question
    f(x,y,z)=Axy^2+Byz+Cx^3*z^2
    given data: at point(1,2,-1) the maximum pointed devertive of f is
    at direcation
    x=0 y=0 z=1
    and its value is 32
    so what are they A,B ,C?

    the only thing i know that since the func is differncial
    32=(0,0,1)*grad f
    and from here we get
    B-C=16

    but how do we get 2 more equation?
    i dunno how to use the data that this is the max pointed devertive
     
  2. jcsd
  3. Sep 13, 2004 #2

    arildno

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    Remember that the gradient must be parallell to the direction of maximal "pointed" derivative!
    The gradient is therefore:
    [tex]\nabla{f}=(0,0,32)[/tex]
    Hence, you get 3 equations with 3 unknowns, one equation for each component.
     
  4. Sep 13, 2004 #3

    ori

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    thank u
    how did u do the formula? (with the grad symbol)
     
  5. Sep 13, 2004 #4

    HallsofIvy

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    He used \nabla in a "tex" formula.

    Click on any "tex" formula and you will see the code used.
     
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