Let a,b R and f: R R be defined by f(x)=a (|x^3-x|)+b|x| (|x^3+x|). Then f is

JEE Advanced 2016 Mathematics question

Let and be defined by . Then is

Answer: (A),(B)

Cosine is even, so , differentiable everywhere. Since has the same sign as , ; for , ,

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Question ID VK-026581