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

  • question_answer
    The number of points at which the function \[f(x)=\left| x-0.5 \right|+\left| x-1 \right|+\tan x\] does not have a derivative in the interval (0, 2) is

    A) 0

    B) 1

    C) 2

    D) 3

    Correct Answer: D

    Solution :

    [d] \[\left| x-a \right|\] is not differentiable at x = a. Also tan x is not differentiable if \[x=(2k+1)\frac{\pi }{2},k\in I\] \[\therefore \] In the interval (0, 2), f(x) is not derivable at \[x=0.5,x=1\] and \[x=\frac{\pi }{2}\]


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