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Gradient math problem help

  1. Feb 28, 2009 #1
    1. The problem statement, all variables and given/known data

    Consider the function f (x,y). if you start at the point (4,5) and move to the point (5,6) . the directional derivative is 2. Starting at the point (4,5) and moving toward the point (6,6)gives a directional derivative of 3.Find grad f at the point (4,5) .

    2. Relevant equations



    3. The attempt at a solution
    I don't really know how to go about this question. All I can do so far is find the unit vector.
    PQ = (5-4) i + (6-5) j = i+j ; u = 1/sqrt 2 i + 1/sqrt 2 j

    PR = (6-4 i +( 6-5) j = 2i+j ; u = 2/sqrt 5 i + 1/sqrt 5 j
     
    Last edited by a moderator: Jul 20, 2014
  2. jcsd
  3. Feb 28, 2009 #2

    Dick

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    Re: Gradients

    If the gradient G=ai+bj, then the given information tells you PQ.G=2 and PR.G=3. That's two equations in two unknowns.
     
  4. Feb 28, 2009 #3
    Re: Gradients

    Use the equation [tex]f_u = \nabla f \cdot u[/tex]. You'll set yourself up with a system of equations, solve them, and you're done.
     
  5. Feb 28, 2009 #4
    Re: Gradients

    ok i set the system of equation and i'm getting nowhere.
    grad f1 = .5i + .5j
    grad f2 = .2981i + .1491j
    how do i set up the system of equation.
     
  6. Feb 28, 2009 #5

    Dick

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    Re: Gradients

    Those aren't the right equations. E.g. PQ.G doesn't have i or j in it.
     
    Last edited: Feb 28, 2009
  7. Feb 28, 2009 #6

    HallsofIvy

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    Re: Gradients

    Write the gradient as [itex]f\vec{i}+ g\vec{j}[/itex].

    1. What is the unit vector in the direction from (4, 5) to (5, 6)? What is the dot product of that vector with [itex]f\vec{i}+ g\vec{j}[/itex]? Set that equal to 2.

    2. What is the unit vector in the direction from (4, 5) to (6, 6)? What is the dot product of that vector with [itex]f\vec{i}+ g\vec{j}[/itex]? Set that equal to 3.

    You now have two equations to solve for f and g.
     
  8. Feb 28, 2009 #7
    Re: Gradients

    I got it now, thank you so much.
     
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