Question

For the function f(x,y)= x+e^(xy) find a vector u ≠ 0 which is orthogonal to ∇f(0,1).

Answer 1

you must find \[\nabla f (0,1)\] before.
\[\nabla f (x,y)=(1+ye^{xy},xe^{xy})\]
Thus \[\nabla f (0,1)=(2,0)\]
Then we can find easily a vector which is orthogonal to (2,0)

Answer 2

How do i find the vector orthogonal to (2.0)?

Answer 3

you know \[\vec{a}.\vec{b}=0\] iff \[x.x'+y.y'=0\]

Answer 4

So an orthogonal vector would be (0,1)?

Answer 5

2.x'+0.y'=0
So it's (0,y'), for all \[y' \in R\].

Answer 6

(0,1) may be called a unit vector of (0,y') :)

Answer 7

thanks :)

Answer 8

you're welcome :)