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Applications of Derivative: 4.1 Maximum and Minimum Values ITK-122 Calculus Dicky Dermawan www.dickydermawan.net78.net dickydermawan@gmail.com

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Intro Some of the most important applications of differential calculus are optimization problems, in which we are required to find the optimal (best) way of doing something. Here are examples of such problems that we will solve in this chapter: What is the shape of a can that minimizes manufacturing costs? What is the maximum acceleration of a space shuttle? (This is an important question to the astronauts who have to withstand the effects of acceleration.)

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Definition

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Definition Minimum value 0, no maximumNo minimum, no maximum

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This function has minimum value f(2)=0, but no maximum value. This continuous function g has no maximum or minimum

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Exercises

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Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Section 9.5: Critical Points and Optimization.

Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Section 9.5: Critical Points and Optimization.

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