- #1
lys04
- 70
- 3
- Homework Statement
- can someone give me some intuition about the gradient vector?
This is what I know so far: for a function of two variables f(x,y), the components of the gradient vector at a point represents the partial derivatives at that point, which is how much the function changes when I move a x or y a little bit, keeping the other variable constant. If the partial derivative is negative, that means f will increase if i move in the negative x/y direction and vice versa if it is positive, then that means f will increase when i move in the positive x/y direction.
For example if the gradient vector is (-2, 1) at (1,1), this means if I move in the negative x direction by 1 unit then z increases by 2 unit; and if I move 1 unit in the positive y direction then z increases by 1 unit.
What I don't get is why (-2,1) becomes the direction (x,y) should move in to yield the greatest increase of f?
- Relevant Equations
- ∇f(x,y)=(f_x(x,y), f_y(x,y))
In Homework Statement