The profit-maximisation problem (for production of one good) is introduced as motivation for the development of general optimisation techniques. The general concept of a critical (or stationary) point is presented, together with the method for finding such points and classifying their nature in two different ways: by examining the sign of the derivative around the point and by using the second-derivative test. Optimisation on intervals and infinite intervals is then discussed (where the end-points must be taken into consideration). Additional economic and financial applications are given.
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