# Thread: 2nd derivative test for multi-variable functions

1. ## 2nd derivative test for multi-variable functions

The determinant of the Jacobian of a function can be used, in 2D anyway, to determine whether stationary points are minima, maxima, or saddle points.

Is there a corresponding test for higher dimensions? Clearly there will be many types of saddle points but a point either is or is not a local minima or maxima.

Do the conditions of the 2D test extend to higher dimensions?