[tex]f(x) = -\frac{1}{3}x^{2}+bx+1\\\\a = -\frac{1}{3}\\x = 6 = p\\\\p = \frac{-b}{2a} \ \ |\cdot2a\\\\-b = p\cdot2a\\\\-b = 6\cdot2\cdot(-\frac{1}{3})\\\\-b = -4 \ \ /:(-1)\\\\\boxed{b = 4}[/tex]
