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The maximum value of `f(x)=tan^(-1)(((sqrt(12)-2)x^2)/(x^2+2x^2+3))`isA. `18^(@)`B. `36^(@)`C. `22.5^(@)`D. `15^(@)` |
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Answer» Correct Answer - D `f(x) = tan^(-1). (((sqrt12 - 2)x^(2))/(x^(4) + 2x^(2) + 3))` `= tan^(-1) ((2(sqrt3 -1))/(x^(2) + (3)/(x^(2)) + 2))` As `x^(2) + (3)/(x^(2)) ge 2 sqrt3` [using A.M. `ge` G.M.] `rArr x^(2) + (3)/(x^(2)) + 2 ge 2 + 2 sqrt3` `:. (f(x))_("max") = tan^(-1) ((2(sqrt3 -1))/(2(sqrt3 + 1)))` `= (pi)/(12)` |
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