CUET · MATHS · PYQ PAPER 2025
For \(x>0\), the minimum value of \(\frac{x}{\log _e x}\) is
- A \(\frac{1}{e}\)
- B \(2 e\)
- C \(e\)
- D \(\frac{2}{e}\)
Answer & Solution
Correct Answer
(C) \(e\)
Step-by-step Solution
Detailed explanation
\(f'(x) = \frac{d}{dx}\left(\frac{x}{\ln x}\right) = \frac{(\ln x)(1) - x(\frac{1}{x})}{(\ln x)^2} = \frac{\ln x - 1}{(\ln x)^2}\) \(\frac{\ln x - 1}{(\ln x)^2} = 0 \Rightarrow \ln x - 1 = 0 \Rightarrow \ln x = 1 \Rightarrow x = e\) Minimum value:…
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