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BITSAT2013MathematicsApplication of DerivativesActual

The function f ( x )=( x ( x -2))² is increasing in the set

Options

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

Correct answer

C. (0,1) (2, )

Step-by-step solution

array l Here, f ( x )=( x ( x -2))² f ^ ( x )=4 x ( x -2)( x -1) array For f ( x ) as increasing, f ^ ( x )>0 So, 4 x(x-1)(x-2)>0 x(x-1)(x-2)>0 From the above figure required interval is, (0,1) (2, )

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