Q105 / 160 · AP EAMCET 2019 (20 Apr Shift 1) · Mathematics

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

  • A
    1
  • B
    2
  • C
    3
  • Correct answer
    D
    4

Solution

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.

Hence, the correct answer is option: 'D'.

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