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Direction of maximum increase and rate of change

  1. Nov 17, 2011 #1
    1. The problem statement, all variables and given/known data


    2. Relevant equations


    3. The attempt at a solution

    We find [itex]\nabla f(1,2)[/itex] at point P: the answer is [itex](-4, 13)[/itex]. Now, we know that the directional derivative of f is given by: [itex]\nabla f(1, 2) |u| \cos\theta[/itex]
    where [itex]|u| = 1[/itex] and [itex]\cos\theta=1[/itex] (since the direction is maximized at [itex]\theta\ = 0[/itex] or [itex]\cos\theta=1[/itex])
    So, letting [itex]u[/itex] be the direction of maximum increase:

    [itex]u =[/itex] [itex]\frac {(-4, 13)}{\sqrt{185}}[/itex]

    Is that true (for the first part)? And how can I start with the second? Any help is appreciated. Oh, and [itex]u[/itex] in the first part is irrelevant of the [itex]u[/itex] in the second part of the question.
    Last edited: Nov 17, 2011
  2. jcsd
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