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

  • question_answer
    The value of \[\frac{d}{dx}[|x-1|+|x-5|]\] at \[x=3\] is [MP PET 2000]

    A)            ? 2

    B)            0

    C)            2

    D)            4

    Correct Answer: B

    Solution :

               \[f(x)=|x-1|+|x-5|\]            \[f(x)=\left\{ \begin{align}   & -(x-1)-(x-5),\,\,\,x<1 \\  & \,\,\,\,(x-1)-(x-5),\,\,\,1<x<5 \\  & \,\,\,\,\,\,\,x-1+x-5,\,\,\,\,x>5 \\ \end{align} \right.\]            \[f(x)=\left\{ \begin{matrix}    6-2x, & x<1  \\    4\,\,\,\,\,\,, & 1<x<5  \\    2x-6, & x>5  \\ \end{matrix} \right.\]            \[\because \]  \[x=3\in (1,\,5)\],  \ For x = 3,  \[f(x)=4,\ \ f'(x)=0\].


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