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AP EAMCET201825 Apr 2018Morning ShiftMathematicsApplication of DerivativesActual

The interval in which the function f x = 2 x 2 - log x , for x > 0 decreases is

Options

  1. A( 2 , 4 )
  2. B0 , 1 4
  3. C1 2 , ∞
  4. D0 , 1 2

Correct answer

D. 0 , 1 2

Step-by-step solution

Given: f x = 2 x 2 - log x f ' x = 4 x - 1 x Function is decreasing when f ' x < 0 4 x - 1 x < 0 ⇒ 4 x 2 - 1 < 0 ⇒ x 2 < 1 4 ⇒ x ∈ - 1 2 , 1 2 . But, x > 0 Therefore, f x is decreasing when x ∈ 0 , 1 2 .

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