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JEE Main & Advanced Mathematics Differentiation Question Bank Derivative at a point Standard Differentiation

  • question_answer
    The differential coefficient of the function \[|x-1|+|x-3|\] at the point \[x=2\] is           [RPET 2002; Pb. CET 2000, 04]

    A)            ? 2

    B)            0

    C)            2

    D)            Undefined

    Correct Answer: B

    Solution :

               \[f(x)=|x-1|+|x-3|\]            \[f(x)=\left\{ \begin{matrix}    -(x-1)-(x-3), & x<1  \\    (x-1)-(x-3), & x>1  \\    (x-1)-(x-3), & x<3  \\    (x-1)+(x-3), & x>3  \\ \end{matrix} \right.\]\[=\left\{ \begin{matrix}    4-2x, & x<1  \\    2\,\,\,\,\,\,\,\,\,, & 1<x<3  \\    2x-4, & x>3  \\ \end{matrix} \right.\]                    At\[x=2\], \[f(x)=\]2. Hence \[\,{f}'(x)=0\].


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