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Directional derivative, help

  1. Feb 21, 2015 #1
    1. The problem statement, all variables and given/known data
    [tex]D_{u}(f)(a,b) = \triangledown f(a,b)\cdot u[/tex]

    [tex]D_{(\frac{1}{\sqrt2}, \frac{1}{\sqrt2})}(f)(a,b) = 3 \sqrt{2}[/tex]

    where [tex]u = (\frac{1}{\sqrt2}, \frac{1}{\sqrt2})[/tex]

    find [tex]\bigtriangledown f(a.b)[/tex]

    2. Relevant equations


    3. The attempt at a solution

    first you change grad f into it's partial derivative form and then take the dot product:

    (df/dx, df/dy).(1/root2, 1/root2) = 3root2

    you'll find that:

    df/dx + df/dy = 6

    where would I go from here? quite confused.
     
  2. jcsd
  3. Feb 21, 2015 #2

    Ray Vickson

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    There are infinitely many different gradient vectors that satisfy the given condition. You need more conditions in order to get a unique answer.
     
  4. Feb 21, 2015 #3
    so is my solution complete? if not, where would I obtain more equations to make the conditions more robust?

    you could say that:

    grad f(6-y, y) . (1/root2, 1/root2) = 3root2
     
  5. Feb 21, 2015 #4

    Ray Vickson

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    You cannot pull more information out of the air; somebody has to give it to you. If they do not give you more information, you have gone as far as you can go.
     
  6. Feb 21, 2015 #5
    great, so df/dx + df/dy = 6 is the final solution?

    sorry for bugging you, this question is quite important to me.
     
  7. Feb 21, 2015 #6

    Ray Vickson

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    Asked and answered.
     
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