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BITSAT2023MathematicsApplication of DerivativesActual

The function f(x)= ⁻¹( x+ x) is an increasing function in

Options

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

Correct answer

B. (- 2 , 4 )

Step-by-step solution

Since, f(x)= ⁻¹( x+ x) f ^ ( x )= 1 1+( x + x )^2 ( x - x ) = 2 (x+ 4 ) 1+( x+ x)^2 f(x) is increasing if f^ (x)>0 (x+ 4 )>0 - 2 < x+ 4 < 2 - 3 2 < x+ 4

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