Question

Tìm max,min:

a) A = \(\left(2x-1\right)\left(x-3\right)\)

b) B = \(\left(1-2x\right)\left(x-3\right)\)

Answer 1

a) A = (2x−1)(x−3)

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

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

dấu = xảy ra khi x=\(\frac{7}{4}\)

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

b) B = (1−2x)(x−3)

=\(x-3+6x-2x^2=-\left(2x^2-7x+3\right)\)

=\(-\left(\sqrt{2}x-\frac{7}{2\sqrt{2}}\right)^2\)+\(\frac{49}{8}-3\)<=25/8

dấu = xảy ra khi x=7/4

=> Max B =25/8 khi x=7/4