Some classical examples of problem solving, where an extreme value condition is required, are here
considered and/or revisited. The search for non-calculus solutions appears pedagogically useful and
intriguing as shown through a rich literature. A teacher, who teaches both maths and physics, (as
happens in Italian High schools) can find in these kinds of problems a mind stimulating exercise
compared with the standard solution obtained by the differential calculus. A good link between the
geometric and analytical explanations is so established.