a, \(A=\left|x+2\right|+\left|x-3\right|-7\)
\(=\left|x+2\right|+\left|3-x\right|-7\)
\(\ge\left|x+2+3-x\right|-7=5-7=-2\)
\(minA=-2\Leftrightarrow\left(x+2\right)\left(3-x\right)\ge0\Leftrightarrow-2\le x\le3\)
b, \(B=-\frac{5}{x^2+4}\ge-\frac{5}{0+4}=-\frac{5}{4}\)
\(minB=-\frac{5}{4}\Leftrightarrow x=0\)
c, \(C=-x^2+6x-4y^2-4y+5\)
\(=-\left(x-3\right)^2-\left(2y+1\right)^2+15\le15\)
\(maxC=15\Leftrightarrow\left\{{}\begin{matrix}x-3=0\\2y+1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=-\frac{1}{2}\end{matrix}\right.\)