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anonymous

  • 5 years ago

T(x,y,z) = 1/(1 + x^2 + y^2 + z^2) where T is measured in degrees Celsius and x,y,z in meters. In which direction does the temperature increase fastest at the point (1,1,-2)? What is the maximum rate of increase?

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  1. anonymous
    • 5 years ago
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    I could a brief explanation of what to do, don't have to give a full explanation just get me started. Already found the gradient vector of T, plugged in the point, used my own directional vector u = <x,y,z> to get a new function F as a function of the derivative in any given direction, tried to maximize and failed. ended up with gradient(F) = <-1/22, -1/22, 1/11> What now?

  2. anonymous
    • 5 years ago
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    For this information, you must give me your soul.

  3. anonymous
    • 5 years ago
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    Hahaha. Seriously, I could use some help.

  4. anonymous
    • 5 years ago
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    And you think I'm not serious?

  5. anonymous
    • 5 years ago
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    Shows how much help you really need...

  6. anonymous
    • 5 years ago
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    Directional derivatives require me to go back half a semester and look up notes from then.

  7. anonymous
    • 5 years ago
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    Directional Derivative is just the dot product of the vector function and a directional vector.

  8. anonymous
    • 5 years ago
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    Okay... And... Doesn't help me at all/you don't know what I'm talking about. Give me your soul if you want help or else start crying.

  9. anonymous
    • 5 years ago
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    Cool story bro. Go troll someone else.

  10. anonymous
    • 5 years ago
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    Take the magnitude of your gradient vector to find maximum rate of change, it seems like you already know what to do.

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