COMEDK · Maths · 27. Application of Derivatives
\(f(x)=2 x-\tan ^{-1} x-\log (x+\sqrt{x^2+1}) \text { is monotonically increasing, when }\)
- A \(x>0\)
- B \(x \in R-\{0\}\)
- C \(x<0\)
- D \(x \in R\)
Answer & Solution
Correct Answer
(D) \(x \in R\)
Step-by-step Solution
Detailed explanation
The function is given by \(f(x) = 2x - \tan^{-1} x - \log(x + \sqrt{x^2 + 1})\). To determine the interval where \(f(x)\) is monotonically increasing, we find its derivative \(f'(x)\) with respect to \(x\).…
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