Đáp án:
$\begin{array}{l}
a)A = 5x - {x^2}\\
= - \left( {{x^2} - 5x} \right)\\
= - \left( {{x^2} - 2.x.\dfrac{5}{2} + \dfrac{{25}}{4}} \right) + \dfrac{{25}}{4}\\
= - {\left( {x - \dfrac{5}{2}} \right)^2} + \dfrac{{25}}{4} \le \dfrac{{25}}{4}\\
\Leftrightarrow GTLN:A = \dfrac{{25}}{4}\,khi:x = \dfrac{5}{2}\\
b)B = x - {x^2}\\
= - \left( {{x^2} - x} \right)\\
= - \left( {{x^2} - 2.x.\dfrac{1}{2} + \dfrac{1}{4}} \right) + \dfrac{1}{4}\\
= - {\left( {x - \dfrac{1}{2}} \right)^2} + \dfrac{1}{4} \le \dfrac{1}{4}\\
\Leftrightarrow GTLN:B = \dfrac{1}{4}khi:x = \dfrac{1}{2}\\
c)C = 4x - {x^2} + 3\\
= - \left( {{x^2} - 4x + 4} \right) + 7\\
= - {\left( {x - 2} \right)^2} + 7 \le 7\\
\Leftrightarrow GTLN:C = 7khi:x = 2\\
d)D = - {x^2} + 6x - 11\\
= - \left( {{x^2} - 6x + 9} \right) - 3\\
= - {\left( {x - 3} \right)^2} - 3 \le - 3\\
\Leftrightarrow GTLN:D = - 3khi:x = 3\\
e)E = 5 - 8x - {x^2}\\
= - \left( {{x^2} + 8x + 16} \right) + 21\\
= - {\left( {x + 4} \right)^2} + 21 \le 21\\
\Leftrightarrow GTLN:E = 21khi:x = - 4\\
f)F = 4x - {x^2} + 1\\
= - \left( {{x^2} - 4x + 4} \right) + 5\\
= - {\left( {x - 2} \right)^2} + 5 \le 5\\
\Leftrightarrow GTLN:F = 5khi:x = 2
\end{array}$
