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Thread: directional dervitives.

  1. #1
    Member zangestu888's Avatar
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    directional dervitives.

    given f(x,y)=x^2+y^2-2x-4y find all points at which the direction of the directional dervitive of fastest change u=i + j, i did the maximinzing the directional dervitive and stuff i got all points on the line 1-x=y the book has y=1+x wheres is my mistake? ! thanks
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by zangestu888 View Post
    given f(x,y)=x^2+y^2-2x-4y find all points at which the direction of the directional dervitive of fastest change u=i + j, i did the maximinzing the directional dervitive and stuff i got all points on the line 1-x=y the book has y=1+x wheres is my mistake? ! thanks
    and how exactly did you get to your answer? note that the direction of greatest increase is the direction $\displaystyle \nabla f$. Now, since we want this to be parrallel to $\displaystyle u = i + j$, it means we need the i-component to be the same as the j-component.

    Now, $\displaystyle \nabla f = \left< 2x - 2, 2y - 4 \right>$

    and so we require $\displaystyle 2x - 2 = 2y - 4$
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