Explanation Given the equation of deflection as y = k ( 2 x 4 − 5 L x 3 + 3 L 2 x 2 ) . Differentiate y with respect to x . y = k ( 2 x 4 − 5 L x 3 + 3 L 2 x 2 ) d y d x = k ( 2 ( 4 x 3 ) − 5 L ( 3 x 2 ) + 3 L 2 ( 2 x ) ) d y d x = k ( 8 x 3 − 15 L x 2 + 6 L 2 x ) In order to obtain maxima and minima put d y d x = 0 . k ( 8 x 3 − 15 L x 2 + 6 L 2 x ) = 0 8 x 3 − 15 L x 2 + 6 L 2 x = 0 x ( 8 x 2 − 15 L x + 6 L 2 ) = 0 So, either x = 0 or ( 8 x 2 − 15 L x + 6 L 2 ) = 0 . Use the quadratic formula x = − b ± b 2 − 4 a c 2 a and solve the equation ( 8 x 2 − 15 L x + 6 L 2 ) = 0 as shown below. From equation ( 8 x 2 − 15 L x + 6 L 2 ) = 0 , note that a = 8 , b = − 15 L and c = 6 L 2 . Substitute a = 8 , b = − 15 L and c = 6 L 2 in above expression. x = 15 L ± ( 15 L ) 2 − 4 ( 8 ) ( 6 L 2 ) 2 ( 8 ) = 15 L ± 225 L 2 − 192 L 2 16 = 15 L − 33 L 2 16 , 15 L + 33 L 2 16 = 9.25 L 16 , 20.74 L 16 Hence, x = 0 , 0.578 L , a n d 1 .296L . Differentiate d y d x with respect to x . d 2 y d x 2 = d ( x ( 8 x 2 − 15 L x + 6 L 2 ) ) d x = 8 x 2 − 15 L x + 6 L 2 + x ( 8 ( 2 x ) − 15 L ) = 8 x 2 − 15 L x + 6 L 2 + 16 x 2 − 15 L x = 24 x 2 − 30 L x + 6 L 2 Substitute x = 0 in d 2 y d x 2

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 24.7, Problem 35E

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Chapter 24.7, Problem 34E

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Chapter 24 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 24.1 - For the parabola y = 4 − x2, at the point (3, −5)...Ch. 24.1 - Prob. 2PE Ch. 24.1 - Prob. 1E Ch. 24.1 - Prob. 2E Ch. 24.1 - Prob. 3E Ch. 24.1 - Prob. 4E Ch. 24.1 - Prob. 5E Ch. 24.1 - Prob. 6E Ch. 24.1 - Prob. 7E Ch. 24.1 - Prob. 8E

Ch. 24.1 - Prob. 9E Ch. 24.1 - Prob. 10E Ch. 24.1 - Prob. 11E Ch. 24.1 - Prob. 12E Ch. 24.1 - In Exercises 11–14, find the equations of the...Ch. 24.1 - Prob. 14E Ch. 24.1 - Prob. 15E Ch. 24.1 - Prob. 16E Ch. 24.1 - Prob. 17E Ch. 24.1 - Prob. 18E Ch. 24.1 - Prob. 19E Ch. 24.1 - Prob. 20E Ch. 24.1 - Prob. 21E Ch. 24.1 - Where does the normal line to the parabola y = x —...Ch. 24.1 - Prob. 23E Ch. 24.1 - Prob. 24E Ch. 24.1 - A certain suspension cable with supports on the...Ch. 24.1 - Prob. 26E Ch. 24.1 - Prob. 27E Ch. 24.1 - Prob. 28E Ch. 24.1 - Prob. 29E Ch. 24.1 - Prob. 30E Ch. 24.2 - In Example 1, let x1 = 0.3, and find x2. 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