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MHT CET202121 Sep 2021Evening ShiftMathematicsApplication of DerivativesActual

The function f ( x )= (1+ x )- 2 x 2+ x is increasing on

Options

  1. A(- , )
  2. B(-5, )
  3. C(- , 0)
  4. D(-1, )

Correct answer

D. (-1, )

Step-by-step solution

aligned & f ( x )= (1+ x )- 2 x 2+ x x -2 & aligned f ^ ( x ) & = 1 (1+ x ) - [ (2+ x )(2)-(2 x )(1) (2+ x )^2 ] & = 1 1+ x - [ 4 (2+ x )^2 ]= ( x +2)^2-4( x +1) ( x +2)^2(1+ x ) aligned aligned When f^ (x)>0 , we write x^2 (x+2)^2(1+x) >0 Since x^2>0 and (x+2)^2>0 , we write (1+x)>0 x>-1

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