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Gradient of a zero function

  1. Jan 15, 2013 #1
    Suppose F(x,y,z) = 0
    grad (F) = 0 ???

    e.g. F = x + y + z

    grad (F) = <1,1,1> =/= <0,0,0> ??

    I don't know why I get an opposite result
     
  2. jcsd
  3. Jan 16, 2013 #2

    SteamKing

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    What opposite result are you talking about?

    The derivative of a constant is always zero, regardless of the value of the constant.

    Hint: F(x,y,z) = x + y + z is not a constant function.
     
  4. Jan 16, 2013 #3

    lurflurf

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    grad(x+y+z)=<1,1,1> =/= <0,0,0> =grad(0)
    x+y+z=/=0

    There is no contradiction, why would you expect one?
     
  5. Jan 16, 2013 #4
    Because if ##F(x,y,z)=x+y+z## then it's not a zero function? And it doesn't have a critical point at (0,0,0) either. Maybe I'm not clear what exactly what you're asking. ##F(x,y,z)=x+y+z## equals zero at zero but the value of a function at one point doesn't tell you anything about the value of its derivative. Derivatives depend on the value of a function in the neighbourhood of the point.
     
  6. Jan 16, 2013 #5

    HallsofIvy

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    Hamjoop, could you please come back and explain more about what you are asking/thinking? A "zero function", to me, is exactly what it says: F(x,y,z)= 0 for all x, y, and z. And that is certainly not true for F(x,y,z)= x+ y+ z. What is your idea of a "zero function"?
     
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