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COMEDK2024MathematicsApplication of DerivativesActual

The function y= x-x is

Options

  1. Adecreasing in (0, 4 ) and increasing in ( 4 , 2 )
  2. Ba decreasing function in (0, 2 )
  3. Can increasing function in (0, 2 )
  4. Dincreasing in (0, 4 ) and decreasing in ( 4 , 2 )

Correct answer

C. an increasing function in (0, 2 )

Step-by-step solution

Let f(x) = x - x . To determine the intervals of increase or decrease, find the first derivative of f(x) with respect to x . f'(x) = d dx ( x - x) = ^2 x - 1 . Using the trigonometric identity ^2 x - 1 = ^2 x , we have f'(x) = ^2 x . For x (0, 2 ) , x > 0 , which implies ^2 x > 0 . Since f'(x) > 0 for all x (0, 2 ) , the function f(x) = x - x is strictly increasing in the interval (0, 2 ) . Answer: an increasing function in (0, 2 )

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