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Gradient and parallel points of a function

  1. Oct 6, 2011 #1
    1. The problem statement, all variables and given/known data
    Find the set of points where the gradient of f is parallel to u =(1,1) for
    f(x,y)=x2 + y3 + 2xy

    2. Relevant equations
    the gradient of f(x,y)=((partial derivative of f wrt x), (partial derivative of f wrt y))
    u=grad f

    3. The attempt at a solution
    fx = 2x+2y
    fy = 3y+2x



    I set the partials equal to the respective values of u and solved and got one set of points. I have a feeling this is wrong. I got x= 1/2 and y= 0

    I looked through the notes and cannot find anything to help me with this so I came here in hope of getting pointed in the right direction.
    Last edited: Oct 6, 2011
  2. jcsd
  3. Oct 6, 2011 #2


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    You don't need grad(f) = u, they're just parallel, so grad(f) = c*u, for any scalar c.
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