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JEE Main & Advanced Mathematics Limits, Continuity and Differentiability Question Bank Self Evaluation Test - Continuity and Differentiability

  • question_answer
    Which one of the following functions is differentiable for all real values of x?

    A) \[\frac{x}{\left| x \right|}\]

    B) \[x\left| x \right|\]

    C) \[\frac{1}{\left| x \right|}\]

    D) \[\frac{1}{x}\]

    Correct Answer: B

    Solution :

    [b] Since \[\frac{x}{\left| x \right|}\] is not continuous function \[\therefore \] it is not differentiable also. Also, L.H.D. and R.H.D. at \[x=0\] not equal. Thus, only function given in option ?b? gives differentiability for all real values of x.


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