If the Lagrange function L corresponding to the problem of extremizing f(x, y, z) subject to the constraint g(x, y, z) = 0 has exactly two critical points, then f must attain its maximum value at one of the points and attain its minimum value at the other point.

Question

Quizplus · Accepted Answer

The existence of exactly two critical points of the Lagrange function does not guarantee that one will be a maximum and the other a minimum of the function f under the constraint. The nature of these critical points (whether they are maxima, minima, or saddle points) depends on further analysis, such as the second derivative test or other criteria.

If the Lagrange Function L Corresponding to the Problem of Extremizing