The number of points, where the function f : R R, f(x) = |x − 1| cos|x − 2| sin|x − 1| + (x - 3)|x^ 2 - 5x + 4|, is NOT differentiable, is :

JEE Main 2022 Mathematics question

The number of points, where the function f : , f(x) = |x − 1| cos|x − 2| sin|x − 1| + + 4|, is NOT differentiable, is :

(1)1
(2)2Correct
(3)3
(4)4

Answer: (2)

Solution

f(x) = |x − 1| cos|x − 2| sin|x − 1| + (x − 3)|x − 1||x − 4| = |x − 1|[cos|x − 2| sin|x − 1| + (x − 3)|x − 4|]. The factor |x − 1| is not differentiable at x = 1, where the bracket is non-zero, and |x

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Question ID VK-035153