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AP EAMCET201823 Apr 2018Morning ShiftMathematicsApplication of DerivativesActual

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

Options

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

Correct answer

D. (0, 1 2 )

Step-by-step solution

We have, f(x)=2 x^2- x, x>0 Differentiate w.r.t ' x ' f^ (x)=4 x- 1 x = 4 x^2-1 x Now, f^ (x)=0 4 x^2-1=0 4 x^2=1 x= 1 2 for decreasing aligned f^ (x) & 0 aligned So, x (0, 1 2 )

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