COMEDK · Maths · 27. Application of Derivatives
The maximum value of \(\frac{\log x}{x}\) in \((2, \infty)\) is
- A 1
- B \(\frac{2}{e}\)
- C \(e\)
- D \(\frac{1}{e}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{e}\)
Step-by-step Solution
Detailed explanation
We have, \[ \begin{aligned} f(x) &=\frac{\log x}{x} \\ \Rightarrow f^{\prime}(x) &=\frac{\frac{1}{x} \times x-\log x \cdot 1}{x^{2}}=\frac{1-\log x}{x^{2}} \end{aligned} \] For maxima or minima,…
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