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COMEDK202510 May 2025Evening ShiftMathematicsApplication of DerivativesActual

In the interval (0,1) the function f(x)=x^2-x+1 is

Options

  1. AIncreasing
  2. BNeither increasing nor decreasing
  3. CStrictly decreasing
  4. DDecreasing

Correct answer

B. Neither increasing nor decreasing

Step-by-step solution

The function is given by f(x) = x^2 - x + 1 . To determine the monotonicity of the function, we find its derivative with respect to x : f'(x) = d dx (x^2 - x + 1) = 2x - 1 . We analyze the sign of f'(x) in the interval (0, 1) . For 0 For 1 2 1 , which implies 2x - 1 > 0 . Thus, f'(x) > 0 in the interval ( 1 2 , 1) , meaning the function is strictly increasing in this sub-interval. Since the derivative changes sign within the interval (0, 1) , the function is neither increasing nor decreasing on the entire interval

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