Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. More Applications of the Derivative Prepared.

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Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. More Applications of the Derivative Prepared by: Midori Kobayashi Humber College C29

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd Rate of Change

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd EXAMPLE 2-Page 828

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd EXAMPLE 3-Page 828

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd EXAMPLE 3-Page 828-Continued Ohm’s Law v = Ri

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd EXAMPLE 3-Page 828-Continued Power P = vi

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd EXAMPLE 3-Page 828-Continued

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd EXAMPLE 5-Page 830

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd Motion of a Point

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd EXAMPLE 7-Page 832

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd EXAMPLE 8-Page 833

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd EXAMPLE 13-Page 836

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd Related Rates

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd EXAMPLE 14-Page 838

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd EXAMPLE 14-Page 838 -continued

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd EXAMPLE 15-Page 840

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd EXAMPLE 15-Page 840- continued

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd EXAMPLE 16-Page 841 (AB) 2 =A 2 B 2

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd EXAMPLE 16-Page 841- continued

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd Optimization

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd EXAMPLE 17-Page 845 Minimize the sum

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd EXAMPLE 17-Page 845-Continued Find the critical values Must be positive!

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd EXAMPLE 17-Page 845-Continued Need to be tested if this point is a minimum Concave up! x =10

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd EXAMPLE 18-Page 846 Maximum volume! By product rule!

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd EXAMPLE 18-Page 846-Continued If x =20, 40 – 2(20) =0 (length cannot be 0!)

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd EXAMPLE 20-Page 847 Maximum Strength! with some constant k 30.0

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd EXAMPLE 20-Page 847-Continued Must be positive!

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd EXAMPLE 20-Page 847-Continued Need to be tested if this point is a minimum Concave down! x =17.3

Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. Copyright Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. Copyright © 2008 John Wiley & Sons Canada, Ltd. All rights reserved. Reproduction or translation of this work beyond that permitted by Access Copyright (The Canadian Copyright Licensing Agency) is unlawful. Requests for further information should be addressed to the Permissions Department, John Wiley & Sons Canada, Ltd. The purchaser may make back-up copies for his or her own use only and not for distribution or resale. The author and the publisher assume no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information contained herein.