Question

Tìm GTLN:

A=4x-x²

B=-9x²+6x-2

Answer 1

A=4x-x²

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

\(=4-\left(x^2-4x+4\right)\)

\(=4-\left(x-2\right)^2\le4\)

Dấu = khi x=2

Vậy Max_A=4 khi x=2

b)-9x²+6x-2

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

\(=-9\left(x-\frac{1}{3}\right)^2-1\le-1\)

Dấu = khi \(x=\frac{1}{3}\)

Vậy Max_B=-1 khi \(x=\frac{1}{3}\)

 

Answer 2

\(A=4x-x^2=4-x^2+4x-4=4-\left(x-2\right)^2\ge4\)

\(M\text{ax}A=4\Leftrightarrow x=2\)

\(B=-9x^2+6x-2=-1-9x^2+6x-1=-1-\left(3x-1\right)^2\ge-1\)

\(M\text{ax}B=-1\Leftrightarrow x=\frac{1}{3}\)