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BITSAT2023MathematicsApplication of DerivativesActual

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

Options

  1. A(0, )
  2. B(- , 0)
  3. C(- , )
  4. DNone of these

Correct answer

A. (0, )

Step-by-step solution

Given f(x)= (1+x)- 2 x 2+x aligned & f^ (x)= 1 1+x - (2+x)(2)-2 x (2+x)^2 & = 1 1+x - 4 (2+x)^2 & = (2+x)^2-4-4 x (1+x)(2+x)^2 = x^2 (1+x)(2+x)^2 >0 for all & x (0, ) aligned Thus, given function f ( x ) is increasing on (0 , ) .

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