Question

1/Tìm gtnn hoặc gtln của biểu thức sau

-3x²+2x-1

Answer 1

Đặt \(A=-3x^2+2x-1\)

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

\(=-3\left(x^2-2.x.\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{2}{9}\right)\)

\(=-3\left[\left(x-\dfrac{1}{3}\right)^2+\dfrac{2}{9}\right]\)

\(=-3\left(x-\dfrac{1}{3}\right)^2-\dfrac{2}{3}\)

Ta có: \(-3\left(x-\dfrac{1}{3}\right)^2\le0\)

\(\Rightarrow A=-3\left(x-\dfrac{1}{3}\right)^2-\dfrac{2}{3}\le\dfrac{-2}{3}\)

Dấu " = " xảy ra khi \(-3\left(x-\dfrac{1}{3}\right)^2=0\Leftrightarrow x=\dfrac{1}{3}\)

Vậy \(MAX_A=\dfrac{-2}{3}\) khi \(x=\dfrac{1}{3}\)

Answer 2

Gtnn và gtln là j vậy ?