imo class 12 continuity and differentiability

If f(x) = |x − 2| + |x − 5|, then f is not differentiable at:

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If f(x) = |x − 2| + |x − 5|, then f is not differentiable at:

  • A. x = 2, 5
  • B. x = 0
  • C. x = 2 only
  • D. x = 5 only

Answer: A) x = 2, 5

Explanation: Absolute value function sum has sharp corners at each critical point, x=2 and x=5.

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