Question

Tìm max, min: a) A= (2x - 1)(x - 3)

                        b) B= (1 - 2x)(x - 3)

Answer 1

                       : a) A= (2x - 1)(x - 3)

A=\(2x^2-6x-x+3=\left(2x^2-\frac{2.\sqrt{2}.7}{2\sqrt{2}}x+\frac{49}{8}\right)-\frac{49}{8}+3\)

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

dấu = xảy ra khi \(x=\frac{7}{4}\)

=> Min A=\(-\frac{25}{8}\)khi x=\(\frac{7}{4}\)

                        b) B= (1 - 2x)(x - 3)

=\(-2x^2+6x+x-3\)

=\(-\left(2x^2-7x+\frac{49}{8}\right)-3-\frac{49}{8}\)

=\(-\frac{73}{8}-\left(\sqrt{2}x-\frac{7}{2\sqrt{2}}\right)^2\)<= \(-\frac{73}{8}\)

dấu = xảy ra khi x=\(\frac{7}{4}\)

=> MaxB=-73/8 khi x=7/4