I am trying to find the extrema of a function on a particular set. I used the Lagrange multiplier method and found 2 points. Now I want to classify those points. Should I just put them in the function and determine which one is maximum and which one is minimum according to the function value at those 2 points? Or is there a possibility that one of them is actually a saddle point?
Can a critical point found by Lagrange multipliers method be a saddle point
lagrange multipliermultivariable-calculus
Best Answer
If your set is closed and bounded, there is no need for that: your function has to have a maximum and a minimum there, and one of those two points that you were able to find must then be the point at which the maximum is attained, whereas the other one must be the point at which the minimum was attained.