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MHT CET202311 May 2023Evening ShiftMathematicsDifferentiationActual

The set of all points, where the derivative of the functions f (x)= x 1+|x| exists, is

Options

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

Correct answer

A. (- , )

Step-by-step solution

f (x) can be written as aligned & f (x)= array l x 1-x , x 0 x 1+x , x>0 array . & f ^ (x)= cases (1-x)+x (1+x)^2 , & x 0 (1+x)-x (1+x)^2 , & x>0 cases & f ^ (x)= 1 (1+x)^2 x (- , ) aligned Derivative of f (x) exists x (- , )

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