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Azteck

  • 3 years ago

If \[x_{1}, x_{2},...,x_{n}\] are given numbers, show that \[(x_{1}-x)^{2} +(x_{2}-x)^{2}+...+(x_{n}-x)^{2}\] is least when x is the arithmetic mean of \[x_{1}, x_{2},..., x_{n}.

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  1. Azteck
    • 3 years ago
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    \[x_{1}, x_{2},..., x_{n}\]

  2. LogicalApple
    • 3 years ago
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    Let S be the summation \[S = (x _{1} - x)^{2} + (x _{2} - x)^{2} + . . . + (x _{n} - x)^{2}\] Find the derivative of S

  3. LogicalApple
    • 3 years ago
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    Remember that the only variable here is x, all the x's with subscripts are constants.

  4. Azteck
    • 3 years ago
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    Yep. I'm just getting the sum of that AP

  5. Azteck
    • 3 years ago
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    Yeah this one was easier than the question before. Thanks.

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