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The greatest integer function defined by f(x) = [x], 0 < x < 2 is

  1. Neither continuous nor differentiable at x = 1
  2. Continuous but not differentiable at x = 1
  3. Not continuous but differentiable at x = 1
  4. Both continuous and differentiable at x = 1

Answer (Detailed Solution Below)

Option 1 : Neither continuous nor differentiable at x = 1
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Detailed Solution

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Calculation:-

[x] function can be drawn as

F1 A.K 9.4.20 Pallavi D1

Let us check the continuity

f(x) at x + 1 = 0

∴ The function is not continuous, which is also evident from the graph as well.

As, the function is not continuous,

∴ it will not be differentiable as well.

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