The function $x-\frac{\log(1+x)}{x}(x>

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Applications of Derivatives

Question:

The function $x-\frac{\log(1+x)}{x}(x>0)$ is increasing in:

Options:

(1, ∞)

(0, ∞)

(2, 2e)

(1/e , 2e)

Correct Answer:

(0, ∞)

Explanation:

$f'(x)=\frac{x-\frac{\log(1+x)}{x}+\log(1+x)}{x^2}>0$ for increasing function $f'(x)>0$

$⇒x^2-\frac{x}{1+x}+\log(1+x)>0⇒x>0\,x∈(0, ∞)$