- #1

xWaffle

- 30

- 0

## Homework Statement

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) = x

^{2}/2 - y

^{2}/2; (√2, 1)

## Homework Equations

∇f = (∂f/∂x)

**i**+ (∂f/∂y)

**j**

## The Attempt at a Solution

∇g = <x, -y>

∇g(√2, 1) = <√2, -1>

_______________________

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.