\(A=\left(x-1\right)\left(x+6\right)\left(x+2\right)\left(x+3\right)\)
\(A=\left(x^2+5x-6\right)\left(x^2+5x+6\right)=\left(x^2+5x\right)^2-36\ge-36\)
\(\Rightarrow A_{min}=-36\) khi \(x^2+5x=0\Rightarrow\left[{}\begin{matrix}x=0\\x=-5\end{matrix}\right.\)
\(B=x^2-4x+4-3=\left(x-2\right)^2-3\ge-3\)
\(\Rightarrow B_{min}=-3\) khi \(x-2=0\Rightarrow x=2\)
\(C=\frac{-4}{x^2-4x+4+6}=\frac{-4}{\left(x-2\right)^2+6}\ge-\frac{2}{3}\)
\(\Rightarrow C_{min}=-\frac{2}{3}\) khi \(x=2\)
\(D=\frac{-2}{x^2-x+\frac{1}{4}+\frac{3}{4}}=\frac{-2}{\left(x-\frac{1}{2}\right)^2+\frac{3}{4}}\ge\frac{-2}{\frac{3}{4}}=\frac{-8}{3}\)
\(\Rightarrow D_{min}=-\frac{8}{3}\) khi \(x=\frac{1}{2}\)
