The set of all point., where the function f(x)=x1+|x| is differentiable, Is

The set of all point., where the function f(x)=x1+|x| is differentiable, Is

  1. A

    ,

  2. B

    (0,)

  3. C

    (,0)(0,)

  4. D

    (,1)(1)

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    Solution:

    We have,

    f(x)=x1+|x|=g(x)h(x), where g(x)=x,h(x)=1+|x|

     Tearly, g(x) is differentiable on (,). The domain of h(x) is 

    x,). Since |x| is not differentiable at x=0. Therefore, h(x)

     not differentiable at x=0. Thus, f(x) is differentiable on 

    ,0)(0,)

     At x=0, we have 

    limx0f(x)f(0)x0=limx0x1+|x|x=limx011+|x|=1

     Therefore, f(x) is differentiable at x=0

     Hence, f is differentiable on (,)

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