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Math Help - 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 \nabla f. Now, since we want this to be parrallel to u = i + j, it means we need the i-component to be the same as the j-component.

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

    and so we require 2x - 2 = 2y - 4
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