The function f(x)=|x^2-3x+2|+ |x| is not differentiable at x=

JEE Advanced Mathematics question

The function is not differentiable at

(A)
(B)
(C)Correct
(D)Correct

Answer: (C),(D)

Solution

(cosine is even), which is differentiable everywhere. , so . The modulus of a polynomial is non-differentiable exactly at its simple (sign-changing) roots, here . At and , , so is differentiable (e.g.

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Question ID VK-109341