TS EAMCET · Maths · Application of Derivatives
The maximum value of \(\frac{\log x}{x}, 0 < x < \infty\) is
- A \(\infty\)
- B \(e\)
- C 1
- D \(e^{-1}\)
Answer & Solution
Correct Answer
(D) \(e^{-1}\)
Step-by-step Solution
Detailed explanation
Let \(\quad y=\frac{\log x}{x}\) \(\Rightarrow \quad \frac{d y}{d x}=\frac{x \cdot \frac{1}{x}-\log x}{x^2}=\frac{1-\log x}{x^2}\) Put \(\quad \frac{d y}{d x}=0 \Rightarrow \log x=1\) \(\Rightarrow \quad x=e\) Now,…
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