# Simple Gradient Question (funtion of two variables)

1. Sep 20, 2012

### xWaffle

1. The problem statement, all variables and given/known data
Find the gradient of the function at the given point. Then sketch the gradient together with the level curve that passes through the point.

g(x,y) = x2/2 - y2/2; (√2, 1)

2. Relevant equations
∇f = (∂f/∂x)i + (∂f/∂y)j

3. The attempt at a solution
∇g = <x, -y>
∇g(√2, 1) = <√2, -1>
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Am I done with this solution? Or is there more I need to put for the gradient at the point?

I'm not really sure if this needs to be reduced to a single number or not, I'm guessing that has to do with my lack of understand of the gradient itself. I thought I was supposed to have a direction vector, is it implied the direction vector is just u = i + j if it is not specified?

I also have no idea how to draw what it's asking. I can't visualise any of this.

2. Sep 20, 2012

### HallsofIvy

Staff Emeritus

You are confusing this with the derivative "in the direction of unit vector v". That is equal to $v\cdot \nabla f$.

3. Sep 20, 2012

### 4189

Yes, the gradient you calculated is correct.