Maximum value of logx/x in interval [2 ,

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Applications of Derivatives

Question:

Maximum value of logx/x in interval [2 , ∞] is

Options:

log2/2

1/e

Correct Answer:

Explanation:

$f'(x)=\frac{1}{x^2}(1-\ln x)$

Clearly f(x) increasing for x < e and decreases for x > e

⇒ x = e is the point of local maxima

∴ maximum f(x) = $\frac{1}{e}$

Hence (4) is the correct answer.