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ALGEBRA(Sum of Absolute Value Differences)

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As x ranges over all real values, what is the minimum value of f(x)=x−123+x−456+x−789?

  • ALGEBRA(Sum of Absolute Value Differences) -

    Note that |x-a|+|x-b| is constant (b-a) for a<=x<=b

    So, since |x-123|+|x-789| is constant for 123<=x<=789, the minimum occurs at x=456, and is 666.

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