imo class 12 application of derivatives

The minimum value of f(x) = |x − 1| + |x − 2| + |x − 3| is:

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The minimum value of f(x) = |x − 1| + |x − 2| + |x − 3| is:

  • A. 2
  • B. 1
  • C. 3
  • D. 4

Answer: A) 2

Explanation: f(x) is sum of distances from 1, 2, 3. The minimum occurs at median x = 2. f(2) = |2−1| + |2−2| + |2−3| = 1 + 0 + 1 = 2.

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