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

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Presentation on theme: "Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. More Applications of the Derivative Prepared."— Presentation transcript:

1 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

2 Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. 29.1 29.1 Rate of Change

3 Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. 29.1-EXAMPLE 2-Page 828

4 Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. 29.1-EXAMPLE 3-Page 828

5 Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. 29.1-EXAMPLE 3-Page 828-Continued Ohm’s Law v = Ri

6 Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. 29.1-EXAMPLE 3-Page 828-Continued Power P = vi

7 Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. 29.1-EXAMPLE 3-Page 828-Continued

8 Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. 29.1-EXAMPLE 5-Page 830

9 Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. 29.2 29.2 Motion of a Point

10 Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. 29.2-EXAMPLE 7-Page 832

11 Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. 29.2-EXAMPLE 8-Page 833

12 Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. 29.2-EXAMPLE 13-Page 836

13 Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. 29.3 29.3 Related Rates

14 Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. 29.3-EXAMPLE 14-Page 838

15 Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. 29.3-EXAMPLE 14-Page 838 -continued

16 Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. 29.3-EXAMPLE 15-Page 840

17 Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. 29.3-EXAMPLE 15-Page 840- continued

18 Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. 29.3-EXAMPLE 16-Page 841 (AB) 2 =A 2 B 2

19 Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. 29.3-EXAMPLE 16-Page 841- continued

20 Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. 29.4 29.4 Optimization

21 Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. 29.4-EXAMPLE 17-Page 845 Minimize the sum

22 Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. 29.4-EXAMPLE 17-Page 845-Continued Find the critical values Must be positive!

23 Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. 29.4-EXAMPLE 17-Page 845-Continued Need to be tested if this point is a minimum Concave up! Min @ x =10

24 Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. 29.4-EXAMPLE 18-Page 846 Maximum volume! By product rule!

25 Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. 29.4-EXAMPLE 18-Page 846-Continued If x =20, 40 – 2(20) =0 (length cannot be 0!)

26 Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. 29.4-EXAMPLE 20-Page 847 Maximum Strength! with some constant k 30.0

27 Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. 29.4-EXAMPLE 20-Page 847-Continued Must be positive!

28 Calter & Calter, Technical Mathematics with Calculus, Canadian Edition ©2008 John Wiley & Sons Canada, Ltd. 29.4-EXAMPLE 20-Page 847-Continued Need to be tested if this point is a minimum Concave down! Max @ x =17.3

29 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.

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