Potential Energy - Finding Balance Points

[Jalo]

Homework Statement

Consider the force F=(y²z³ − 6xz²)i + 2xyz³j + (3xy²z² − 6x²z)k.

I've solved the first part of the problem that asked if the force was conservative (it was) and what was the potential energy of the force(U)

U=-y²z³+3x²z²+c , c E ℝ

Find the balance points.

Homework Equations

The Attempt at a Solution

I know the balance points are gotten trough derivation of U and equalating it to 0. However I don't know what should i use to derivate it with. ∂U/∂x + ∂U/∂y = 0 ? Doesn't help me much... Help would be appreciated.
Thanks

 

[billVancouver]

Hi Jalo,

I find it a bit unclear what 'balance points' refer to here - my only guess is potential minima, which will have to be in all three dimensions at once (not just x and y like you guessed). Consider the gradient of the potential function and see if that leads you anywhere,

Hope this helps,
Bill Mills