The function $(x^2 – 1)|x^2 – 3x + 2| + cos|x|$ is not differentiable at

Q: The function $(x^2 – 1)|x^2 – 3x + 2| + cos|x|$ is not differentiable at

(A) –1

(B) 0

(C) 1

(D) 2

Sol: $ \large f(x) = \left\{\begin{array}{ll} (x^2 – 1)(x-1)(x-2)+ cosx \; , x < 1 , x > 2\\ -(x^2 – 1)(x-1)(x-2)+ cosx \; , 1 \le x \leq 2 \end{array} \right. $

f(x) is differentiable every where possibly not at x = 1, 2.

After testing the condition of differentiability, we can see that f(x) is not differentiable at x = 2 .

Hence (D) is the correct answer.