a.
Do \(\left|x\right|\ge0;\forall x\Rightarrow\left|-x\right|\le0;\forall x\)
Dấu "=" xảy ra khi \(x=0\)
Nên \(A\le-3,5\)
Vậy \(A_{max}=-3,5\) khi \(x=0\)
b.
Do \(\left|\dfrac{2}{3}x+1\right|\ge0;\forall x\)
Dấu "=" xảy ra khi \(\dfrac{2}{3}x+1=0\Rightarrow x=-\dfrac{3}{2}\)
Đồng thời \(-4,5< 0\)
Nên \(-4,5\left|\dfrac{2}{3}x+1\right|\le0\)
Vậy \(B_{max}=0\) khi \(x=-\dfrac{3}{2}\)
c.
Do \(\left\{{}\begin{matrix}-\left|2x-3\right|\le0\\-\left|5y-2\right|\le0\end{matrix}\right.\) ; \(\forall x;y\)
Dấu "=" xảy ra khi \(\left\{{}\begin{matrix}x=\dfrac{3}{2}\\y=\dfrac{2}{5}\end{matrix}\right.\)
Nên \(-\left|2x-3\right|-\left|5y-2\right|+6,5\le6,5\)
Vậy \(C_{max}=6,5\) khi \(\left\{{}\begin{matrix}x=\dfrac{3}{2}\\y=\dfrac{2}{5}\end{matrix}\right.\)
d.
Do \(\left\{{}\begin{matrix}-\left|-y+5\right|\le0\\-\dfrac{1}{2}x^2\le0\end{matrix}\right.\) ;\(\forall x;y\)
Dấu "=" xảy ra khi \(\left\{{}\begin{matrix}x=0\\y=5\end{matrix}\right.\)
nên \(3-\left|-y+5\right|-\dfrac{1}{2}x^2\le3\)
Vậy \(D_{max}=3\) khi \(\left\{{}\begin{matrix}x=0\\y=5\end{matrix}\right.\)
