Chứng minh rằng E = -11 + 6x - x^2 < 0 với mọi x

* Hướng dẫn giải

$\mathrm{E}=-11+6\mathrm{x}-{\mathrm{x}}^2=-\left({\mathrm{x}}^2-6\mathrm{x}+9\right)-2=-{\left(\mathrm{x}-3\right)}^2-2$

Vì $-{\left(\mathrm{x}-3\right)}^2\le 0\left(\forall \mathrm{x}\right)\Rightarrow -{\left(\mathrm{x}-3\right)}^2-2\le -2\left(\forall \mathrm{x}\right)$. Dấu ''='' xảy ra $\iff \mathrm{x}-3=0\iff \mathrm{x}=3$

Vậy $\mathrm{Max}\mathrm{E}=-2\iff \mathrm{x}=3$