Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Applications of Derivatives

Question:
The function \(\frac{\log x}{x}\) attains its maximum at the point
Options:
\(x=e\)
\(x=\frac{1}{e}\)
\(x=\sqrt{e}\)
None of these
Correct Answer:
\(x=e\)
Explanation:
\(\begin{aligned}f^{\prime}(x)&=\frac{1-\log x}{x^{2}}\\ \text{So }f^{\prime}(x)&=0\Rightarrow x=e\\ f^{\prime \prime}(e)&<0\end{aligned}\)