Let f be a function defined by f x -tan -1 x 2- kx -9- x - If range of f x lies in the interval 0- -2 for all values of x - R- then find the maximum integral value of k-

Since range is a subset of (0, π/2) hence x^2 + (k 1)x + 9 gt; 0 ∀ x ϵ R ⇒ D lt; 0 (k 1)^2 36 lt; 0 (k 7) (k + 5) lt; 0 k ( 5, 7) ∴ k_max = ...

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Let f be a fu...

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Let f be a function defined by $f (x) = t a n^{- 1} (x^{2} + k x + 9 - x)$ . If range of f(x) lies in the interval $(0, \frac{π}{2})$ for all values of $x ϵ R$ , then find the maximum integral value of k. ___

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