Giải thích các bước giải:

Ta có:

$A=-3x^2+12x-1=-3(x-2)^2+11\le 11$

$\to GTLN=11\to x-2=0\to x=2$

Ta có:

$B=9+4x-2x^2=11-2(x-2)^2\le 11$

$\to GTLN=11\to x-2=0\t x=2$

Ta có:

$C=9x+2-3x^2=-3(x-\dfrac32)^2+\dfrac{35}4\le\dfrac{35}4$

$\to GTLN=\dfrac{35}4\to x-\dfrac32=0\to x=\dfrac32$

Ta có:

$D=2x-2-3x^2=-3\left(x-\dfrac{1}{3}\right)^2-\dfrac{5}{3}\le-\dfrac53$

$\to GTLN=-\dfrac53\to x-\dfrac13=0\to x=\dfrac13$

Ta có:

$E=7x-3x^2+5=-3\left(x-\dfrac{7}{6}\right)^2+\dfrac{109}{12}\le \dfrac{109}{12}$

$\to GTLN=\dfrac{109}{12}\to x-\dfrac76=0\to x=\dfrac76$

Ta có:

$F=2-2x^2-9x=-2\left(x+\dfrac{9}{4}\right)^2+\dfrac{97}{8}\le\dfrac{97}8$

$\to GTLN=\dfrac{97}8\to x+\dfrac94=0\to x=-\dfrac94$

Ta có:

$G=15+7x-5x^2=-5\left(x-\dfrac{7}{10}\right)^2+\dfrac{349}{20}\le \dfrac{349}{20}$

$\to GTLN=\dfrac{349}{20}$

$\to x-\dfrac7{10}=0\to x=\dfrac7{10}$

Ta có:

$H=10x-6x^2+5=-6\left(x-\dfrac{5}{6}\right)^2+\dfrac{55}{6}\le \dfrac{55}{6}$

$\to GTLN=\dfrac{55}{6}$

$\to x-\dfrac56=0\to x=\dfrac56$

Ta có:

$I=11-5x^2+10x =-5\left(x-1\right)^2+16\le 16$

$\to GTLN=16\to x-1=0\to x=1$

Ta có:

$K=-3x^2-6x-12=-3(x+1)^2-9\le -9$

$\to GTLN=-9\to x+1=0\to x=-1$