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AP EAMCET202422 May 2024Evening ShiftMathematicsApplication of DerivativesActual

The interval containing all the real values of x such that the real valued function f(x)= x + 1 x is strictly increasing is

Options

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

Correct answer

A. (1, )

Step-by-step solution

f(x)= x + 1 x Clearly, f(x) is defined for x 0f^ = 1 2 x - 1 2 x^ -3 / 2 = 1 2 x (1- 1 x ) For f^ (x) 0 We must have (1- 1 x ) 0 x 1 So, f(x) is strictly increasing in (1, )

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