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Diretional Derivative

  1. Nov 23, 2015 #1


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    Having a melt down as I have done this problem twice now and my exam is tomorrow and I can't seem to figure it out anymore.... ugh.

    1. The problem statement, all variables and given/known data

    The depth of a lake at the point on the surface with coordinates (x, y ) is given by D(x, y ) = 100−4x 2 −y 2 . a) If a boat at the point (−1, 2) is sailing in the direction 4~i +~j, is the water getting deeper or shallower ?
    2. Relevant equations
    I know that I need to use the gradient and I am going to need to have the direction scaled to a unit vector.

    3. The attempt at a solution
    So I took the gradient of D(x,y), plugged in (-1,2) then dotted it with the unit vector of (4,1) the answer is supposed to be 28/sqrt(17) and I can't seem to get that answer.
  2. jcsd
  3. Nov 23, 2015 #2


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    never mind, I just kept doing the unit vector wrong. Simple arithmetic mistake.
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