CUET · MATHS · PYQ PAPER 2023
The maximum value of \(\frac{\log x}{x}\) for \(x\) in \([2, \infty)\) is :
- A e
- B \(0\)
- C 1
- D \(\frac{1}{e}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{e}\)
Step-by-step Solution
Detailed explanation
\(f'(x) = \frac{\frac{1}{x} \cdot x - \log x \cdot 1}{x^2} = \frac{1 - \log x}{x^2}\) \(f'(x) = 0 \implies 1 - \log x = 0 \implies \log x = 1 \implies x = e\) \(f(e) = \frac{\log e}{e} = \frac{1}{e}\)
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