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 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?

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JEE Advanced (Single Correct MCQs): Limits, Continuity and Differentiability

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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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