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For \(a > b > c > 0\), the minimum value of the function \(f(x) = |x - a| + |x - b| + |x - c|\) is

Question and options

For a>b>c>0a > b > c > 0, the minimum value of the function f(x)=∣x−a∣+∣x−b∣+∣x−c∣f(x) = |x - a| + |x - b| + |x - c| is
  1. 2a−b−c2a - b - c
  2. a+b−2ca + b - 2c
  3. a+b+ca + b + c
  4. a−ca - c

Answer and explanation

Correct answer: D - \(a - c\)
Sum of distances is minimised at the median x = b: (a-b) + 0 + (b-c) = a - c.

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