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AP EAMCET201822 Apr 2018Evening ShiftMathematicsApplication of DerivativesActual

If x>0 , then x 1+x - (1+x)

Options

  1. Ais less than zero
  2. Bis greater than zero
  3. Cis equal to zero
  4. Dtakes all the real values

Correct answer

A. is less than zero

Step-by-step solution

Let a function f(x)= x 1+x - (1+x) , for x>0 aligned f^ (x) & = (x+1)-x (1+x)^2 - 1 (1+x) & = 1 (1+x)^2 - 1 1+x = 1-(1+x) (1+x)^2 & = -x (1+x)^2 0 aligned f^ (x) 0 f(x) is a strictly decreasing function for x < 0 . Now, f (0⁺ )=0 So, f(x) < 0

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