Gradient Problem Move From P(-1,1)

[Geometrick]

Homework Statement

You are at P(-1,1) on the surface z = (y-x^2)^3. What direction should you move from P so that your height remains the same?

Homework Equations

The Attempt at a Solution

So I basically do not want my height z to change. In this case, I will take a vector perpendicular to grad f(p), a simple computation shows that grad f(p) will be in the direction of <1,2>, so I take my direction v to be v = <-2, 1>.

I'm just wondering if this is correct?

 

[Mark44]

Homework Statement

You are at P(-1,1) on the surface z = (y-x^2)^3. What direction should you move from P so that your height remains the same?

Homework Equations

The Attempt at a Solution

So I basically do not want my height z to change. In this case, I will take a vector perpendicular to grad f(p), a simple computation shows that grad f(p) will be in the direction of <1,2>, so I take my direction v to be v = <-2, 1>.

I'm just wondering if this is correct?

I think you have the basic idea down, but have made a mistake in the "simple" computation. At (-1, 1) the gradient of f is the zero vector. Both components of the gradient have factors of 3(y - x²)². When x = -1, y = 1, this factor is 3(1 - (-1)²)², or 0.