CUET · MATHS · PYQ PAPER 2025
The function \(f(x)=2 \log _e(x-2)-x^2+4 x+1,(x>2)\) is increasing on the interval :
- A \((1,2)\)
- B \((2,6)\)
- C \((2,3)\)
- D \((3, \infty)\)
Answer & Solution
Correct Answer
(C) \((2,3)\)
Step-by-step Solution
Detailed explanation
\(f'(x) = \frac{2}{x-2} - 2x + 4\) \(f'(x) > 0 \implies \frac{2}{x-2} - 2x + 4 > 0\) \(\frac{2 - 2x(x-2) + 4(x-2)}{x-2} > 0\) \(\frac{-2x^2 + 8x - 6}{x-2} > 0\) \(\frac{-2(x-1)(x-3)}{x-2} > 0\) \(\frac{(x-1)(x-3)}{x-2} For \(x>2\): If \(x \in (2,3)\):…
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