I am wondering whether the above statement is true. "A necessary condition for the constrained optimization problem to have a GLOBAL min or max is that..." Should the word local replace global? I am confused about the method of Lagrange Multipliers as well. When we use this method, we get a bunch of points A1,A2,A3,...An. If we then compute f(A1),f(A2),...,f(An) and take the largest and smallest, are these guaranteed to be the GLOBAL max and min, respectively? If not, under what conditions would this be the case? Also, when using the Lagrange Multipliers method, do we still need to check all the boundary points separately? Could someone explain? I would really appreciate!