a) $A=-x^2-2x+5$
$=-(x^2+2x+1-6)$
$=-(x+1)^2+6$
Vì $(x+1)^2≥0$ nên $A≤6$, dấu "=" xảy ra khi $x+1=0 ⇔ x=-1$
Vậy GTLN là $6$ khi $x=-1$
b) $B=9x+3x^2+4$
$=3\Bigg(x^2+2x.\dfrac{3}{2}+\dfrac{9}{4}\Bigg)-\dfrac{11}{4}$
$=3\Bigg(x+\dfrac{3}{2}\Bigg)^2-\dfrac{11}{4}$
Vì $\Bigg(x+\dfrac{3}{2}\Bigg)^2≥0$ nên $B≥-\dfrac{11}{4}$
Dấu "=" xảy ra khi $x+\dfrac{3}{2}=0 ⇔ x=-\dfrac{3}{2}$
Vậy GTNN là $-\dfrac{11}{4}$ khi $x=-\dfrac{3}{2}$
