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Need help with gradient question.

  1. Jun 3, 2012 #1
    1. The problem statement, all variables and given/known data

    I have been able to solve all the gradient problems when you are given the starting point, and the actual function. But I am getting caught up on this one which goes in reverse


    Suppose that the maximum rate of change of f at (1,-1) is 25 and it occurs in the direction of 3i ⃗-4j ⃗

    b) Find ∇f at (1,-1). c) Find [itex] f_x [/itex](1,-1). d) Find [itex]f_y (1,-1) [/itex].

    2. Relevant equations


    Well I know that [itex]∇f* u = |∇f| [/itex]
    and I think we know that [itex] f_x^2 + f_y^2 = |∇f^2| [/itex]

    3. The attempt at a solution
    Thus I set up the system of equations and solved the quadratic which resulted. However this seemed wrong to me, and I wanted to double check that what I attempted here was correct. Also it seemed like this question should have an easier way to come about a solution. Any guidance would be appreciated

    Thank you.
     
    Last edited: Jun 3, 2012
  2. jcsd
  3. Jun 3, 2012 #2
    How about if you scale the vector (3,-4) to have length 25?

    Hint: what is it's length right now?

    (Details: the gradient at a point, points in the direction of steepest change, and it's length is the rate of change of f if we head a unit in that direction. Thus this is the magnitude and direction. It should be easy to find the x and y components of your gradient.)
     
  4. Jun 3, 2012 #3
    Thanks I got it now. Jeez that was easy like I knew it was. I think I was having a brainfart earlier.
     
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