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

  • question_answer
    The set of all points where \[f(x)=\sqrt[3]{{{x}^{2}}\left| x \right|}-\left| x \right|-1\]is not differentiable is

    A) {0}                  

    B) \[\left\{ -1,\text{ }0,\text{ }1 \right\}\]

    C) {0, 1}  

    D) none of these

    Correct Answer: D

    Solution :

    [d] \[f(x)=\sqrt[3]{{{\left| x \right|}^{3}}}-\left| x \right|-1\] Or \[\left| x \right|-\left| x \right|-1=-1\] Hence, differentiable for all x.


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