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Thread: Multivariable calculus

  1. #1
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    Multivariable calculus

    Prompt: Find points where the fastest change of the function f(x,y) = x^2 + y^2 + x - 2y is in the direction of \vec{v}=<1,2>.

    I'm hoping to get a few pointers on what to do here.
    So far, my strategy is to find the directional derivative of f(x,y) in the direction of \vec{v}.

    D_{u}f(x,y) = \triangledown f(x,y)\cdot\vec{u}, where \vec{u} is the unit vector of \vec{v}.

    Could someone verify if this is the right path, otherwise, I would appreciate just a few hints on what to do here.
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  2. #2
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    Re: Multivariable calculus

    Not totally clear on the question, but I'll give it a shot.

    The gradient of the function is \triangledown f = (2x + 1) u_{x} + (2y - 2) u_{y}

    Since you want to find the point(s) where this function is the greatest, doesn't this mean it has to be differentiated again and then set to 0?
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