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

  • question_answer
    What is the derivative of \[\left| x-1 \right|\] at\[x=2\]?

    A) -1

    B) 0

    C) 1

    D) Derivative does not exist

    Correct Answer: C

    Solution :

    [c] \[f(x)=\left| x-1 \right|\] Redefined the function \[f(x)\] \[f(x)=\left\{ \begin{matrix}    1-x, & x<1  \\    x-1, & x>1  \\ \end{matrix} \right.\] \[f'(x)=\left\{ \begin{matrix}    -1; & x<1  \\    1; & x>1  \\ \end{matrix} \right.\] \[\therefore f'(2)=1\]


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