\(A=6x-x^2-12\\ =-x^2+6x-12\\ =-\left(x^2-6x+12\right)\\ =-\left(x^2-2\times3\times x+9+3\right)\\ =-\left(x^2-2\times3\times x+9\right)-3\\ =-\left(x-3\right)^2-3\le-3\forall x\)
Dấu = xảy ra khi
\(x-3=0\\ =>x=3\)
Vậy \(Max_A=-3\) khi x = 3
A=-(x^2-6x+12)
=-(x^2-6x+9+3)
=-(x-3)^2-3<=-3
Dấu = xảy ra khi x=3