Explanation Given information : f ( x ) = − 2 x 2 Formula needed : d d x ( x n ) = n x n − 1 Calculation : differentiate f ( x ) with respect to x , f ′ ( x ) = d d x ( − 2 x 2 ) = − 2 ( − 2 ) x 3 = 4 x 3 Again, differentiate f ′ ( x ) with respect to x , f ′ ′ ( x ) = d d x ( 4 x 3 ) = 4 ( − 3 ) x 4

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ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 3.2, Problem 23PS

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Tocalculate: f′,f″,f‴, and f(4)

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Chapter 3.2, Problem 22PS

Chapter 3.2, Problem 24PS

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u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (ū+v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅w) Support your answer mathematically or a with a written explanation. d) If possible, find u. (vxw) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Chapter 3 Solutions

Calculus

Ch. 3.1 - Prob. 1PS Ch. 3.1 - Prob. 2PS Ch. 3.1 - Prob. 3PS Ch. 3.1 - Prob. 4PS Ch. 3.1 - Prob. 5PS Ch. 3.1 - Prob. 6PS Ch. 3.1 - Prob. 7PS Ch. 3.1 - Prob. 8PS Ch. 3.1 - Prob. 9PS Ch. 3.1 - Prob. 10PS

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Tocalculate : f ′ , f ″ , f ‴ , and f ( 4 )

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Tocalculate: f′,f″,f‴, and f(4)

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Chapter 3 Solutions