Explanation Given: ( x − x 1 ) 2 + ( x − x 2 ) 2 + ( x − x 3 ) 2 + ... + ( x − x n ) 2 Calculation: The minimum value occurs at the critical point since sum of the squares approaches ∞ , as x → ± ∞ For n = 2 : Let f ( x ) = ( x − x 1 ) 2 + ( x − x 2 ) 2 Differentiating the above equation and equate to zero gives f ' ( x ) = 2 ( x − x 1 ) + 2 ( x − x 2 ) 2 ( x − x 1 ) + 2 ( x − x 2 ) = 0 On solving this equation, we obtain x = 1 2 ( x 1 + x 2 ) For n = 3 : Let f ( x ) = ( x − x 1 ) 2 + ( x − x 2 ) 2 + ( x − x 3 ) 2 Differentiating the above equation and equate to zero gives f ' ( x ) = 2 ( x − x 1 ) + 2 ( x − x 2 ) + 2 ( x − x 3 ) 2 ( x − x 1 ) + 2 ( x − x 2 ) + 2 ( x − x 3

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 4.6, Problem 61E

To determine

To find the value of x that minimizes the sum of the squares (x−x1)2+(x−x2)2+(x−x3)2+...+(x−xn)2.

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Chapter 4.6, Problem 60E

Chapter 4.6, Problem 62E

Chapter 4 Solutions

CALCULUS (CLOTH)

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

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To find the value of x that minimizes the sum of the squares ( x − x 1 ) 2 + ( x − x 2 ) 2 + ( x − x 3 ) 2 + ... + ( x − x n ) 2 .

Solution Summary: The author explains how to determine the value of x that minimizes the sum of the squares.

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To find the value of x that minimizes the sum of the squares (x−x1)2+(x−x2)2+(x−x3)2+...+(x−xn)2.

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