MHT CET · Maths · Application of Derivatives
If \(\mathrm{f}(x)=\log (1+x)-\frac{2 x}{2+x}\) then \(\mathrm{f}(x)\) is increasing in
- A \((-1, \infty)\)
- B \((-\infty, \infty)\)
- C \((0, \infty)\)
- D \((1, \infty)\)
Answer & Solution
Correct Answer
(A) \((-1, \infty)\)
Step-by-step Solution
Detailed explanation
\(f'(x) = \frac{d}{dx}\left(\log(1+x)\right) - \frac{d}{dx}\left(\frac{2x}{2+x}\right)\) \(f'(x) = \frac{1}{1+x} - \frac{2(2+x) - 2x(1)}{(2+x)^2}\)
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