Question

If the maximum value of a, for which the function f_a(x) = tan^-1 2x - 3ax + 7 is non-decreasing in \(\left(-\frac\pi6, \frac \pi6\right)\), is \(\bar a\), then \(f_{\bar a} \left(\frac \pi 8\right)\) is equal to

(A) \(8 - \frac{9\pi}{4(9 + \pi^2)}\)

(B) \(8 - \frac{4\pi}{9(4 + \pi^2)}\)

(C) \(8\left(\frac{1 + \pi^2}{9 + \pi^2}\right)\)

(D) \(8 - \frac\pi4\)

Answer 1

Correct option is (A) \(8 - \frac{9\pi}{4(9 + \pi^2)}\)

Answer 2

option A is Correct