Consider the following in respect of the function f(x)= cases 2+x, & x 0 2-x, & x<0 cases 1. _ x 1 f(x) does not exist. 2. f(x) is differentiable at x=0. 3. f(x) is continuous at x=0. Which of the above statements is/are correct?

NDA 2016 Mathematics question

Consider the following in respect of the function 1. does not exist. 2. is differentiable at . 3. is continuous at . Which of the above statements is/are correct?

(A)1 only
(B)3 onlyCorrect
(C)2 and 3 only
(D)1 and 3 only

Answer: (B)

Solution

. Near the function is , so exists; statement 1 is incorrect. At the left and right limits are both 2 , so

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Question ID VK-028523