Optimisation using calculus

Merced Community College DistrictOptimisation using calculusShairy Balicaoc 2016 Merced CollegeMerced Community College District, Merced College, 20161What is differential calculus used for?1.1IntroductionThe development of mathematics stands as one of the most important achievements ofhumanity, and the development of the calculus, both the differential calculus and integralcalculus is one of most important achievements in mathematics. The practical applications ofdifferential calculus are so wide ranging that it would be impossible to mention them all here.Suffice to say that differential calculus is an indispensable tool in every branch of science andengineering.In elementary mathematics there are two main applications of differential calculus. One is tohelp in sketching curves, and the other is in optimisation problems. In this section we will givea brief introduction to how differential calculus is used in optimisation problems.1.2Optimisation problemsThere are many practical situations in which we would like to make a quantity as small as wepossibly can or as large as we possibly can.For example, a manufacturer of bicycles trying to decide how much to charge for a model ofbicycle would think that if he charges too little for the bicycles then he will probably sell a lotof bicycles but that he won’t make much profit because the price is too low, and that if hecharges too much for the bicycle then he won’t make much profit because … Purchase document to see full attachment

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