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Question: Answered & Verified by Expert
Let \([x]\) denote the greatest integer less than or equal to \(x\). Then the number of points where the function \(y=[x]+|1-x|,-1 \leq x \leq 3\) is not differentiable, is
MathematicsContinuity and DifferentiabilityAP EAMCETAP EAMCET 2019 (20 Apr Shift 1)
Options:
  • A 1
  • B 2
  • C 3
  • D 4
Solution:
1896 Upvotes Verified Answer
The correct answer is: 4
The given function \(y=[x]+|1-x|\) have point of discontinuity at \(x=0,1,2\) and 3 for \(-1 \leq x \leq 3\). So function \(y=[x]+\|-x \mid\) is not differentiable at 4 points. Hence, option (4) is correct.

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