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Application of Derivatives question

2022 · 26 Jul · Shift 2 · Q24

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JEE Main
Mathematics
Application of Derivatives
2022 · 26 Jul · Shift 2 · Q24

Application of Derivatives question

2022 · 26 Jul · Shift 2 · Q24

JEE MainMathematicsApplication of DerivativesMCQ+4 / −1

If the maximum value of

a

, for which the function

f_{a}(x)=\tan ^{-1} 2 x-3 a x+7

is non-decreasing in

\left(-\frac{\pi}{6}, \frac{\pi}{6}\right)

, is

\bar{a}

, then

f_{\bar{a}}\left(\frac{\pi}{8}\right)

is equal to :

A
$8-\frac{9 \pi}{4\left(9+\pi^{2}\right)}$
B
$8-\frac{4 \pi}{9\left(4+\pi^{2}\right)}$
C
$8\left(\frac{1+\pi^{2}}{9+\pi^{2}}\right)$
D
$8-\frac{\pi}{4}$

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