CUET · MATHS · PYQ PAPER 2025
If the maximum value of the function \(f(x)=\frac{2 \log _e x}{x}, x>0\) occurs at \(x=e\), then \(e^3 f^{\prime \prime}(e)\) is equal to
- A \(-2\)
- B \(-\frac{2}{e}\)
- C \(-e\)
- D \(-5 e^3\)
Answer & Solution
Correct Answer
(A) \(-2\)
Step-by-step Solution
Detailed explanation
\(f'(x) = \frac{(\frac{2}{x})x - (2 \log_e x)(1)}{x^2} = \frac{2 - 2 \log_e x}{x^2}\) \(f''(x) = \frac{(-\frac{2}{x})x^2 - (2 - 2 \log_e x)(2x)}{(x^2)^2} = \frac{-2x - 4x + 4x \log_e x}{x^4} = \frac{4 \log_e x - 6}{x^3}\)…
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