Let a, b ∈ R and f : R → R be defined by f(x) = a cos (|x 3…

Maths Functions, Limits, Continuity and Differentiability JEE (Advamced) / IIT - JEE Problems ( Previous Year ) More Than One Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

Let a, b ∈ R and f : R → R be defined by f(x) = a cos (|x 3 –x|) + b|x| sin(|x 3 +x|). Then f is

differentiable at x = 0 if a = 0 and b = 1

differentiable at x = 1 if a = 1 and b = 0

NOT differentiable at x = 0 if a = 1 and b = 0

NOT differentiable at x = 1 if a = 1 and b = 1

Text Solution

Verified by Experts

The correct answer is:

CHECK THE SOLUTION.

(a,b)

Sol. at x = 0, x = 0 is repeated root of g(x) = |x| sin|x 3 + x|

hence f(x) is differentiable

& at x = 1 ⇒ a cos|x 3 – x| = acos(x 3 – x)

as cos(– θ ) = cos( θ ) ∴ f(x) is differentiable

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