If f (x) = x 1+ x x , x (0, 2 ), then
Mathematics · JEE Main · NTA Exams — Limit, Continuity and Differentiability
If f (x) = \(\frac{\mathrm{x}}{1+\mathrm{x} \tan \mathrm{x}}, \mathrm{x} \in\left(0, \frac{\pi}{2}\right),\) then
- f (x) has exactly one point of minimum
- f (x) has exactly one point of maximum
- f (x) is increasing in \(\left(0, \frac{\pi}{2}\right)\)
- maximum occurs at x0 where x0 = cosx0
Answer
(A) f (x) has exactly one point of minimum, (C) f (x) is increasing in (0, 2 )
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