CUET · MATHS · PYQ PAPER 2023
The maximum value of \(\frac{\log x^3}{3 x}\) occurs at \(x=\)
- A \(e\)
- B \(\frac{1}{e}\)
- C \(3 e\)
- D \(\frac{3}{e}\)
Answer & Solution
Correct Answer
(A) \(e\)
Step-by-step Solution
Detailed explanation
\(f(x) = \frac{3 \log x}{3x} = \frac{\log x}{x}\) \(f'(x) = \frac{\frac{1}{x} \cdot x - \log x \cdot 1}{x^2} = \frac{1 - \log x}{x^2}\) \(1 - \log x = 0 \Rightarrow \log x = 1 \Rightarrow x = e\)
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