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For a real number y, let [y] denotes the greatest integer less than or equal to y : Then the function 
  • a)
    discontinuous at some   x
  • b)
    continuous at all x, but the derivative f ' (x) does not exist for some x
  • c)
    f ' (x) exists for all x, but the second  derivative f ' (x) does not exist for some x
  • d)
    f ' (x) exists for all x
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
For a real number y, let [y] denotes the greatest integer less than or...
By def. [x – π] is an integer whatever be the value of x.
And so p[x – π] is an integral multiple of p.
Consequently tan 
And since 1 + [x]2 ≠ 0 for any x, we conclude that f (x) = 0.
Thus f (x) is constant function and so, it is continuous and differentiable any no. of times, that is f '(x), f ''(x), f '''(x),... all exist for every x, their value being 0 at every pt. x. Hence, out of all the alternatives only (d) is correct.
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For a real number y, let [y] denotes the greatest integer less than or equal to y : Then the function a)discontinuous at some xb)continuous at all x, but the derivative f ' (x) does not exist for some xc)f ' (x) exists for all x, but the second derivative f ' (x) does not exist for some xd)f ' (x) exists for all xCorrect answer is option 'D'. Can you explain this answer?
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For a real number y, let [y] denotes the greatest integer less than or equal to y : Then the function a)discontinuous at some xb)continuous at all x, but the derivative f ' (x) does not exist for some xc)f ' (x) exists for all x, but the second derivative f ' (x) does not exist for some xd)f ' (x) exists for all xCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about For a real number y, let [y] denotes the greatest integer less than or equal to y : Then the function a)discontinuous at some xb)continuous at all x, but the derivative f ' (x) does not exist for some xc)f ' (x) exists for all x, but the second derivative f ' (x) does not exist for some xd)f ' (x) exists for all xCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a real number y, let [y] denotes the greatest integer less than or equal to y : Then the function a)discontinuous at some xb)continuous at all x, but the derivative f ' (x) does not exist for some xc)f ' (x) exists for all x, but the second derivative f ' (x) does not exist for some xd)f ' (x) exists for all xCorrect answer is option 'D'. Can you explain this answer?.
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