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

  • question_answer
    The number of values of \[x\in [0,2]\] at which \[f(x)=\left| x-\frac{1}{2} \right|+\left| x-1 \right|+\tan x\] is not differentiable is

    A) 0                     

    B) 1

    C) 3                     

    D) none of these

    Correct Answer: C

    Solution :

    [c] \[\left| x-\frac{1}{2} \right|\] is continuous everywhere but not differentiable at \[x=\frac{1}{2}\], \[\left| x-1 \right|\]is continuous everywhere but not differentiable at x=1, and tan x is continuous in [0, 2] except at \[x=\frac{\pi }{2}\]. Hence, \[f(x)\] is not differentiable at \[x=\frac{1}{2},1,\frac{\pi }{2}.\]


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