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NDA 2016 Maths · Mathematics · Continuity and Differentiability · easy

The function f(x)=|x| is continuous at x=0. 2. The function f(x)=|x| is differentiable at x=0.

Single correct option

Consider the following statements:
1. The function f(x)=∣x∣f(x)=|x| is continuous at x=0x=0.
2. The function f(x)=∣x∣f(x)=|x| is differentiable at x=0x=0.
Which of the statements given above is/are correct?
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (A) 1 only

∣x∣→0=f(0)|x|\to0=f(0) from both sides, so it is continuous at 00. But the left derivative is −1-1 and the right derivative is +1+1, so it is not differentiable at 00. Continuity does not imply differentiability.
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Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake