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JEE Main2006MathematicsContinuity and DifferentiabilityActual

The set of points where f(x)= x 1+|x| is differentiable is

Options

  1. A(- , 0) (0, )
  2. B(- ,-1) (-1, )
  3. C(- , )
  4. D(0, )

Correct answer

C. (- , )

Step-by-step solution

f(x)= array ll x 1-x , & x < 0 x 1+x , & x 0 array f^ (x)= cases 1 (1-x)^2 , & x < 0 1 (1+x)^2 , & x 0 cases . f^ (x) exist at everywhere.

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