Explanation Given Information: Real world problems can be optimized by finding global extrema, critical points or the derivatives Comparing local extrema and end point behavior to find global extrema Strategies for translating real −world problems into mathematical problems Optimizing real −world quantities by solving global extrema point To study the behavior of any function f ( x ) given with in an interval [ a , b ] it is always better to find the critical points such as local maximum and local minimum and the end points. To find global extrema of the function f ( x ) . 1. Take the derivative of f ( x ) 2. Find critical points f ' ( x ) = 0 3. Test the critical points. If f ' ' ( x ) < 0 has a local maximum. If f ' ' ( x ) > 0 has a local minimum. 4. Check height at the local minimum or local maximum. 5. Check height at the end points 6

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 3.4, Problem 0C

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Chapter 3 Solutions

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A summary of “real world problems can be optimized by finding global extrema, critical points or the derivatives”.

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Chapter 3 Solutions