CUET · MATHS · PYQ PAPER 2025
The function \(f(x)=x^2-x+1\) is
- A Increasing on \(\left(-\frac{1}{2}, 1\right)\) and decreasing on \(\left(0, \frac{1}{2}\right)\)
- B Increasing on \(\left(\frac{1}{2}, \infty\right)\) and decreasing on \(\left(-\infty, \frac{1}{2}\right)\)
- C Increasing on \(\left(-\infty, \frac{1}{2}\right]\) and decreasing on \(\left[\frac{1}{2}, \infty\right)\)
- D Increasing on ( \(-\infty, 1\) ) and decreasing on ( \(1, \infty\) )
Answer & Solution
Correct Answer
(B) Increasing on \(\left(\frac{1}{2}, \infty\right)\) and decreasing on \(\left(-\infty, \frac{1}{2}\right)\)
Step-by-step Solution
Detailed explanation
\(f'(x) = 2x - 1\) \(2x - 1 = 0 \Rightarrow x = \frac{1}{2}\) For \(x For \(x > \frac{1}{2}\), \(f'(x) > 0\). Increasing on \(\left(\frac{1}{2}, \infty\right)\).
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