b, B=\(\frac{2}{3}x-2x^2\)+3
= -2(x2-\(\frac{1}{3}x\))+3
=-2(x2-2.\(\frac{2}{3}x+\frac{4}{9}\))+3-(-2.\(\frac{4}{9}\))
=-2(x-\(\frac{2}{3}\))2+\(\frac{35}{9}\le\frac{35}{9}\)
Dấu = xảy ra khi : -2(x-\(\frac{2}{3}\))2=0
\(\Leftrightarrow x=\frac{2}{3}\)
Vậy Max B= \(\frac{35}{9}\Leftrightarrow x=\frac{2}{3}\)
a, Đề ĐÚNG : A=5x2-\(\frac{10}{3}x-1\)
=5(x2-\(\frac{2}{3}x\))-1
=5(\(x^2-2.\frac{1}{3}x+\frac{1}{9}\))-1-5.\(\frac{1}{9}\)
=\(5\left(x-\frac{1}{3}\right)^2-\frac{14}{9}\ge-\frac{14}{9}\)
Dấu = xảy ra khi : 5(x-\(\frac{1}{3}\))2=0
\(\Leftrightarrow x=\frac{1}{3}\)
Vậy MIN A= \(-\frac{14}{9}\Leftrightarrow x=\frac{1}{3}\)