JEE Main 202226 Jul, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002If the maximum value of aaa, for which the function fa(x)=tan−12x−3ax+7f_{a}(x)=\tan ^{-1} 2 x-3 a x+7fa(x)=tan−12x−3ax+7 is non-decreasing in (−π6,π6)\left(-\frac{\pi}{6}, \frac{\pi}{6}\right)(−6π,6π), is aˉ\bar{a}aˉ, then faˉ(π8)f_{\bar{a}}\left(\frac{\pi}{8}\right)faˉ(8π) is equal to :AOption A. 8−9π4(9+π2)8-\frac{9 \pi}{4\left(9+\pi^{2}\right)}8−4(9+π2)9πBOption B. 8−4π9(4+π2)8-\frac{4 \pi}{9\left(4+\pi^{2}\right)}8−9(4+π2)4πCOption C. 8(1+π29+π2)8\left(\frac{1+\pi^{2}}{9+\pi^{2}}\right)8(9+π21+π2)DOption D. 8−π48-\frac{\pi}{4}8−4πCheckSkip · show solution
