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Math Help - Directional derivatives

  1. #1
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    Directional derivatives

    Let f be a differentiable function of two variables, and supposed that del f(p) is not the zero vector. For what directions is the directional derivative of f a maximum, a minimum, zero, and half of its maximum value?

    I'm not entirely sure how solve this problem.

    I know that del f cos theta has a maximum at 1 and a minimum at pi. Is this what the problem is asking?
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  2. #2
    MHF Contributor Calculus26's Avatar
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    max rate

    The maximum rate of change is in the direction of the gradient and the max rate of decrease is opposite to the gradient

    |fu|= |gradf||u|cos(theta) is a max when theta = 0 recall |u| = 1
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