The function $f(x)=\frac{x}{\log x}$ inc

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Applications of Derivatives

Question:

The function $f(x)=\frac{x}{\log x}$ increases on the interval

Options:

$(0, ∞)$

$(0, e)$

$(e, ∞)$

None of these

Correct Answer:

$(e, ∞)$

Explanation:

Clearly, $f(x)$ is defined for $x > 0$

Now, $f(x)=\frac{x}{\log x}⇒f'(x)=\frac{\log x-1}{(\log x)^2}$

$∴f '(x) > 0⇒\log x −1> 0⇒\log x > 1⇒x > e⇒x∈(e, ∞)$