The function given by y = ||x| − − 1| is differentiable for…

Maths Functions, Limits, Continuity and Differentiability General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 12, 2026

The function given by y = ||x| − − 1| is differentiable for all real numbers except the points

{0, 1, − − 1}

− − 1

Text Solution

Verified by Experts

The correct answer is:

Given function is y = | |x| − − 1 |

Here Ly’ ( − − 1) = − − 1 and Ry’ ( − − 1) = 1

Ly’ (0) = 1 and Ry’ (0) = − − 1 and Ly’(1) = − − 1 and Ry’(0) = 1

⇒ ⇒ y is not differentiable at x = − − 1, 0, 1. ∴ ∴ is the correct option

ALTERNATIVE :

Graph of y = | |x| − − 1| is as follows:

Which has sharp turnings at x = − − 1, 0 and 1 and hence not differentiable at x = − − 1, 0, 1.

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