Thread: Third-Order Partial Derivatives

Hi. For a two-variable function, at point Z all first-partials are zero, all second-order-partials are zero, but fxxx (third-order-partial) is non-zero. Is Z is local minimum, maximum, or neither?

I can't use the second derivative test because it's 0 which is inconclusive.

I think it could either be a minimum or maximum. But I don't know why...

Are you familiar with the Hessian determinant?