1. ## 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

2. Originally Posted by zangestu888
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 $2x - 2 = 2y - 4$