When judging the extreme value of multivariate function, the point where the first derivative value is zero is the stagnation point, but it is not necessarily the extreme point. To judge whether it is an extreme value, we need to borrow sufficient conditions for the existence of extreme values of multivariate functions. This theorem can be found in Shu Gao, so that the function value of the second derivative of this function to xx is a at stagnation point, the function value of the second derivative of this function to xy is b at stagnation point, and the function value of the second derivative of this function to yy is at stagnation point.

The value of (1) AC-B 2 is greater than 0 and has an extreme value, which is the largest when A is less than 0 and the smallest when A is greater than 0.

(2) The value of AC-B2 is less than 0, and there is no extreme value.

(2) The value of AC-B2 is equal to 0, which may or may not have extreme value and needs to be discussed separately.