AP EAMCET · Maths · Application of Derivatives
If \(\log (1+x)-\frac{2 x}{2+x}\) is increasing, then
- A \(0 < x < \infty\)
- B \(-\infty < x < 0\)
- C \(-\infty < x < \infty\)
- D \(-1 < x < 2\)
Answer & Solution
Correct Answer
(C) \(-\infty < x < \infty\)
Step-by-step Solution
Detailed explanation
Let \(f(x)=\log (1+x)-\frac{2 x}{2+x^2}\) \[ f^{\prime}(x)=\frac{1}{(1+x)}-\frac{2}{2+x}+\frac{2 x}{(2+x)^2} \] For increasing function, \(f^{\prime}(x)>0\)…
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