Consider the following statements in respect of f(x)=|x|-1 : 1. f(x) is continuous at x=1. 2. f(x) is differentiable at x=0. Which of the above statements is/are correct?

NDA 2021 Mathematics question

Consider the following statements in respect of : 1. is continuous at . 2. is differentiable at . Which of the above statements is/are correct?

(A)1 onlyCorrect
(B)2 only
(C)Both 1 and 2
(D)Neither 1 nor 2

Answer: (A)

Solution

Statement 1: is continuous everywhere, so is continuous at every point, in particular at (near , ). Correct. Statement 2: at , the right-hand derivative is

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Question ID VK-033687