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Math Help - Multi-Variable Calculus-Directional Deriative

  1. #1
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    Multi-Variable Calculus-Directional Deriative

    Let be a function with continous partial deriatives in .
    Let , two directions in . Between all the directional deriatives of f in the point P, the maximal value is 11 when the deriative is in the direction of u. What is the value of ?

    I know the maximal value is the value in the gradient...But have no idea how it helps us...

    Hope you'll be able to help me

    Thanks!
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  2. #2
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    The Directional derivative of f(x,y,z) in the direction of the unit vector \vec{v} is the dot product, \nabla f\cdot \vec{v}= |\nabla f| \vec{u}\cdot\vec{v} where \vec{u} is a unit vector in the direction of \nabla f.
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