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JEE Main & Advanced Mathematics Functions Question Bank Differentiability

  • question_answer
    If \[f(x)=x(\sqrt{x}-\sqrt{x+1}),\] then  [IIT 1985]

    A)            \[f(x)\] is continuous but non- differentiable at \[x=0\]

    B)            \[f(x)\] is differentiable at \[x=0\]

    C)            \[f(x)\] is not differentiable at \[x=0\]                                                  

    D)            None of these

    Correct Answer: C

    Solution :

               Since the function is defined for \[x\ge 0\] i.e. not defined for \[x<0\]. Hence the function neither continuous nor differentiable at \[x=0\].


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