Tìm GTLN của biểu thức: P = 4x - x^2 + 3

* Hướng dẫn giải

$\begin{array}{l}\mathrm{P}=4\mathrm{x}-{\mathrm{x}}^2+3=-\left({\mathrm{x}}^2-4\mathrm{x}-3\right)=-\left[\left({\mathrm{x}}^2-2\mathrm{x}.2+2^2\right)-4-3\right]\\ =-{\left(\mathrm{x}-2\right)}^2+7\\ \mathrm{Vì} {\left(\mathrm{x}-2\right)}^2\ge 0\left(\forall \mathrm{x}\right)\Rightarrow -{\left(\mathrm{x}-2\right)}^2\le 0\left(\forall \mathrm{x}\right)\Rightarrow -{\left(\mathrm{x}-2\right)}^2+7\le 7\left(\forall \mathrm{x}\right)\\ \mathrm{Dấu} \text{'}\text{'}=\text{'}\text{'} \mathrm{xảy} \mathrm{ra} \iff \mathrm{x}-2=0\iff \mathrm{x}=2\\ \mathrm{Vậy} \mathrm{Max}\mathrm{P}=7\iff \mathrm{x}=2\end{array}$