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BITSAT2010MathematicsApplication of DerivativesActual

The function ( f ( x )= x -4 x ) is strictly decreasing on

Options

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

Correct answer

A. ( (- 3 , 3 ) )

Step-by-step solution

(f(x)= x-4 x f^ (x)= ^2 x-4 ) When ( - 3 < x < 3 , 1 < x < 2 ) Therefore, (1 < ^2 x < 4 ) ( -3 < ( ^2 x-4 ) < 0 ) Thus, for ( - 3 < x < 3 , f ^ ( x ) < 0 ) Hence, ( f ) is strictly decreasing on ( ( - 3 , 3 ) )

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