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Math Help - maximum rate of incerase

  1. #1
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    maximum rate of incerase

    give that f(x,y) = 5-x^2 -2y^2 and (x', y') = (-1,-1), the direction of the max rate of increase is



    a. (2,4)
    b. (1,2)
    c. (1/5)^(1/2) (1,2)

    isit all or just one of the above?

    i thought the answer should be a. but my notes stats that it is c.

    may i also know what formula i should used to get the direction that is gving zero rate of increase?
    my working:

    this direction would be perpendicular to grad f(x',y') hence we are looking for the tangent vertor which is the directional derivative at (x', y'), and that is equal to 2(5)^(1/2)

    however my answers showed that the answer is plus minus (1/5)^(1/) (2, -1)

    may i know what is wrong with my understanding please?

    thanks!
    Last edited by alexandrabel90; February 27th 2010 at 03:56 AM. Reason: addition to question
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  2. #2
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    Quote Originally Posted by alexandrabel90 View Post
    give that f(x,y) = 5-x^2 -2y^2 and (x', y') = (-1,-1), the direction of the max rate of increase is



    a. (2,4)
    b. (1,2)
    c. (1/5)^(1/2) (1,2)

    is it all or just one of the above?
    Those are all vectors pointing in the same direction! They are all correct answers.
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  3. #3
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    may i know how part c is derived? i understand why part a and b could be the answers but not part c.

    does that mean that eg (1/8)(1,2) can also be the answer since the direction of this vector is (1,2)?

    thank you!
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