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Wicked Quick Question on Gradient

  1. Dec 17, 2008 #1
    I am given some function f(x,y) and I am asked to find what the maximal rate of change is at some point (x0y0) and the direction in which it occurs.

    Is this correct: Maximal rate of change=[itex]|\nabla{f}(x_0,y_0)|[/itex]

    And for the direction, if [itex]\nabla{f}(x_0,y_0)=<a\, ,b\,>[/itex] then the direction is:

    [tex]\frac{<a\, ,b\,>}{|\nabla{f}(x_0,y_0)|}[/tex]

    Thanks!
     
  2. jcsd
  3. Dec 17, 2008 #2
    Just a yes or no will do me.
     
  4. Dec 17, 2008 #3
    Here it comes!
     
  5. Dec 17, 2008 #4

    Dick

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    You know |grad(f)| is correct answer, right? Rate is grad(f).u. Maximal rate is in the grad(f) direction, so u=grad(f)/|grad(f)|. Hence?
     
  6. Dec 17, 2008 #5
    So my direction question is correct too. I just evaluate grad(f) and get some vector and then find the unit vector in that direction. Yes?
     
  7. Dec 17, 2008 #6

    Dick

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    Yep.
     
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