Consider the following statements in respect of the function f(x)=[3x], where [ ] is the greatest integer function : I. f(x) is continuous at x=1/3. II. f(x) is differentiable at x=1/4. Which of the statements given above is/are correct?

NDA 2026 Mathematics question

Consider the following statements in respect of the function , where is the greatest integer function : I. is continuous at . II. is differentiable at . Which of the statements given above is/are correct?

(A)I only
(B)II onlyCorrect
(C)Both I and II
(D)Neither I nor II

Answer: (B)

Solution

is discontinuous exactly where is an integer. At , : the left-hand limit is 0 and the right-hand limit is 1, so is not continuous; Statement I is incorrect. At $x =

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Question ID VK-030454