- #1

- 19

- 7

- Homework Statement
- see post

- Relevant Equations
- ∇f⋅u= Direction vector

The gradient is < (2x-y), (-x+2y-1) >

at P(1,-1) the gradient is <3, -4>

Since ∇f⋅u= Direction vector, it seems that we should set the equation equal to the desired directional derivative.

< 3, -4 > ⋅ < a, b > = 4

which becomes

3a-4b=4

I thought of making a list of possible combinations of a's and b's which satisfy this equation like so

a, b

corresponding direction vector

0, 1

<0, 1>

(4/3), 0

(for which there is no direction vector??)

2, (1/2)

< 4/√17 , 1/√17 >

But it seems that there are an infinite number of possible combinations. And the question is asking for all of them.

Thank you for your assistance.