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Proving inequalities using method of Lagrange multipliers. (English) Zbl 1208.26022

The authors use the method of Lagrange multipliers to find the maximum and minimum of a function \(f(a,b,c)\) subject to \(g(a,b,c)=0\) to obtain an inequality of the form \(\text{minimum} \leq f(a,b,c) \leq \text{maximum}\). They reprove several inequalities of this fashion.

MSC:

26D07 Inequalities involving other types of functions
52A40 Inequalities and extremum problems involving convexity in convex geometry
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