Question

Tìm max, min:

a) A = (2x - 1)(x - 3) 

b) B = (1 - 2x)(x - 3) 

Answer 1

a) A = (2x - 1)(x - 3) 

=2x²-6x-x+3

=2x²-7x+3

\(=2\left(x^2-\frac{7x}{2}+\frac{3}{2}\right)\)

\(=2\left(x^2-\frac{7x}{2}+\frac{49}{16}-\frac{50}{16}\right)\)

\(=2\left(x-\frac{7}{4}\right)^2-\frac{25}{8}\ge0-\frac{25}{8}=-\frac{25}{8}\)

Dấu = khi \(x=\frac{7}{4}\)

Vậy MinA\(=-\frac{25}{8}\) khi \(x=\frac{7}{4}\)

b) B = (1 - 2x)(x - 3) 

=x-3-2x²+6x

=-2x²+7x-3

\(=-2\left(x^2-\frac{7x}{2}+\frac{3}{2}\right)\)

\(=-2\left(x^2-\frac{7x}{2}+\frac{49}{16}-\frac{50}{16}\right)\)

\(=\frac{25}{8}-2\left(x-\frac{7}{4}\right)^2\le\frac{25}{8}-0=\frac{25}{8}\)

Dấu = khi \(x=\frac{7}{4}\)

Vậy MaxA\(=\frac{25}{8}\) khi \(x=\frac{7}{4}\)