Published by:
CGP EDU Academic Team
Published on: August 11, 2026
The function f(x) = (x 2 − − 1) |x 2 − − 3x + 2| + cos (|x|) is NOT differentiable at
Text Solution
Verified by ExpertsThe correct answer is:
D
we have |x| = 
⇒ ⇒ |x 2 − − 3x + 2| = |(x − − 1)(x − − 2)|
= 
As cos ( − − θ θ ) = cos θ θ ⇒ ⇒ cos |x| = cos x
∴ ∴ Given function can be written as
∴ ∴ 
This function is differentiable at all points except possibly at x = 1 and x = 2.
Lf’(1) = 
= − − sin 1
Rf’(1) = 
= − − sin 1
∴ ∴ Lf’(1) = Rf’(1) ∴ ∴ f is differentiable at x = 1.
∴ ∴ Lf’(2) ≠ ≠ Rf’(2) ∴ ∴ f is not differentiable at x = 2.
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