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MHT CET202014 Oct 2020Evening ShiftMathematicsApplication of DerivativesActual

The function f(x)= x- 2 x x+2

Options

  1. Ax (- , 1)
  2. Bx (-1, )
  3. Cx (- , 0)
  4. Dx (0, )

Correct answer

D. x (0, )

Step-by-step solution

aligned Given f(x) &= x- 2 x x+2 f^ (x) &= 1 x - [ (x+2)(2)-(2 x)(1) (x+2)² ] &= 1 x - [ 4 (x+2)² ]= x²+4 x x(x+2)² &= x(x+4) x(x+2)² aligned For f^ (x)>0, x 0 and x>-4 Hence x (0, ) is permissible.

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