On Two Classes of Extremum Problems without Calculus
Murray S. Klamkin · Mathematics Magazine · 1992
Calculus provides us with systematic, general, and powerful methods for attacking extremum problems. Because of its generality, there are often simpler methods for solving specific problems. These usually involve inequalities, e.g., Arithmetic-Geometric Mean (A.M.-G.M.), Jensen, H6lder, Minkowski, or a discriminant. If one surveys the maximum and minimum problems in our calculus texts, one will find that a great many of them can be done much more efficiently just using the A.M.-G.M. inequality in two and three variables, i.e.,