Let f:(−∞,∞)→(−∞,∞) be given by f(x)=x|x|+|x−1|−|x−2|2+|x−3|3 If A denotes the set of points wheref (x) is not differentiable, then A =

Let f:(,)(,) be given by f(x)=x|x|+|x1||x2|2+|x3|3 If A denotes the set of points wheref (x) is not differentiable, then A =

  1. A

    {3}

  2. B

    {1}

  3. C

    {0}

  4. D

    {2}

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    Solution:

    h(x)=x|x|=x2,x0x2,x<0is a differentiable function

    u(x)=|x2|2=(x2)2 is a differentiable function

    v(x)=|x3|3=(x3)3,x3(x3)3,x<3is a differentiable
    function

    w(x)=|x1| is not differentiable at x=1.

    f is differentiable everywhere except at x=1

    Hence A∣={1}

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