\(B\left(1-x\right)\left(3x+4\right)\)

\(\rightarrow B=\frac{1}{3}\left(3-3x\right)\left(3x+4\right)\)

\(\rightarrow B\text{⩽ }\frac{1}{3}\left(\frac{3-3x+3x+4}{2}\right)^2\)

\((BTD\)\(AM-GM)\)

\(\rightarrow B\text{⩽ }\frac{1}{3}.\frac{49}{4}\)

\(\rightarrow B\text{⩽ }\frac{49}{12}\)

Dấu '' = '' xảy ra \(\Leftrightarrow3-3x=3x+4\Leftrightarrow-\frac{1}{6}\)

Vậy \(max\)\(B=\frac{49}{12}\Leftrightarrow x=-\frac{1}{6}\)

\(B=\left(1-x\right).\left(3x+4\right)\)

Ta có :

\(B=3x+4-3x^2-4x\)

\(B=-3x^2-x+4\)

\(B=-3\left(x^2+\frac{1}{3}x-\frac{4}{3}\right)\)

\(B=-3\left(x^2+2.\frac{1}{6}.x+\frac{1}{36}-\frac{1}{36}-\frac{4}{3}\right)\)

\(B=-3\left[\left(x+\frac{1}{6}\right)^2-\frac{49}{36}\right]\)

Vì \(\left(x+\frac{1}{6}\right)^2\ge0\)

\(\Rightarrow\left(x+\frac{1}{36}\right)^2-\frac{49}{36}\ge-\frac{49}{36}\)

\(\Rightarrow B\le\frac{49}{12}\)

\(\Rightarrow\)GTLN của B là \(\frac{49}{12}\)Khi \(x=-\frac{1}{6}\)

\(-2x+4\sqrt{x}+1\)

\(=-2\left(x-2\sqrt{x}+1\right)+3\)

\(=-2\left(\sqrt{x}-1\right)^2+3\le3\left(\forall x\ge0\right)\)

Dấu "=" xảy ra \(\Leftrightarrow\sqrt{x}-1=0\Leftrightarrow\sqrt{x}=1\Leftrightarrow x=1\)

\(A=2x^2-3x+2=2\left(x^2-\frac{3}{2}x\right)+2\)

\(=2\left(x^2-2.\frac{3}{4}x+\frac{9}{16}-\frac{9}{16}\right)+2=2\left(x-\frac{3}{4}\right)^2-\frac{9}{8}+2\ge\frac{7}{8}\)

Dấu ''='' xảy ra khi x = 3/4 

Vậy GTNN của A bằng 7/8 tại x = 3/4