Explanation Calculation: Assume f ( x ) = a n x n + a n − 1 x n − 1 + a n − 2 x n − 2 + ⋯ + a 0 to be the required polynomial of degree n . Here, n is a positive integer, a 0 , a 1 , ⋯ , a n are constants, and a n ≠ 0 . The first derivative of f is, f ′ ( x ) = d d x ( a n x n + a n − 1 x n − 1 + a n − 2 x n − 2 + ⋯ + a 1 x + a 0 ) = d d x a n x n + d d x a n − 1 x n − 1 + d d x a n − 2 x n − 2 + ⋯ + d d x a 1 x + d d x a 0 = a n d d x x n + a n − 1 d d x x n − 1 + a n − 2 d d x x n − 2 + ⋯ + a 1 d d x x + d d x a 0 = a n n x n − 1 + a n − 1 ( n − 1 ) x n − 2 + a n − 2 ( n − 2 ) x n − 3 + ⋯ + a 1 The second derivative of f is, f ″ ( x ) = d d x f ′ ( x ) = d d x ( a n n x n − 1 + a n − 1 ( n − 1 ) x n − 2 + a n − 2 ( n − 2 ) x n − 3 + ⋯ + a 2 2 x + a 1 ) = d d x a n n x n − 1 + d d x a n − 1 ( n − 1 ) x n − 2 + d d x a n − 2 ( n − 2 ) x n − 3 + ⋯ + d d x a 2 2 x + d d x a 1 = a n n d d x x n − 1 + a n − 1 ( n − 1 ) d d x x n − 2 + a n − 2 ( n − 2 ) d d x x n − 3 + ⋯ + a 2 2 d d x x + d d x a 1 Simplify it further

10th Edition

ISBN: 9781337825597

Author: Tan

Publisher: INTER CENG

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Chapter 3.5, Problem 44E

To determine

The given statement “If f is a polynomial of degree n, then f(n+1)(x)=0 ” is true or false.

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Chapter 3.5, Problem 43E

Chapter 3.5, Problem 45E

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Force with 800 N and 400 N are acting on a machine part at 30° and 60°, respectively with the positive x axis

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Chapter 3 Solutions

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Ch. 3.1 - State the following rules of differentiation in...Ch. 3.1 - Prob. 2CQ Ch. 3.1 - Prob. 3CQ Ch. 3.1 - Prob. 4CQ Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E

Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Prob. 48E Ch. 3.1 - Prob. 49E Ch. 3.1 - Prob. 50E Ch. 3.1 - Prob. 51E Ch. 3.1 - Prob. 52E Ch. 3.1 - Prob. 53E Ch. 3.1 - U.K. MOBILE PHONE VIDEO VIEWERS As mobile phones...Ch. 3.1 - Prob. 55E Ch. 3.1 - 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The given statement “If f is a polynomial of degree n , then f ( n + 1 ) ( x ) = 0 ” is true or false.

Solution Summary: The author explains that if f is a polynomial of degree n, the given statement is true or false.

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The given statement “If f is a polynomial of degree n, then f(n+1)(x)=0 ” is true or false.

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Chapter 3 Solutions