Đáp án:
$\begin{array}{l}
h)x - 9{x^2} + 17\\
= - 9{x^2} + x - \dfrac{1}{{36}} + \dfrac{{611}}{{36}}\\
= - {\left( {3x - \dfrac{1}{6}} \right)^2} + \dfrac{{611}}{{36}} \le \dfrac{{611}}{{36}}\\
\Leftrightarrow GTLN = \dfrac{{611}}{{36}},khi\,x = \dfrac{1}{{16}}\\
g) - {x^2} - 3x - 7\\
= - {x^2} - 3x - \dfrac{9}{4} - \dfrac{{19}}{4}\\
= - {\left( {x + \dfrac{3}{2}} \right)^2} - \dfrac{{19}}{4} \le - \dfrac{{19}}{4}\\
\Leftrightarrow GTLN = - \dfrac{{19}}{4},khi\,x = - \dfrac{3}{2}\\
i) - {x^2} - 7x + 25\\
= - {x^2} - 7x - \dfrac{{49}}{4} + \dfrac{{149}}{4}\\
= - {\left( {x + \dfrac{7}{2}} \right)^2} + \dfrac{{149}}{4} \le \dfrac{{149}}{4}\\
\Leftrightarrow GTLN = \dfrac{{149}}{4},khi\,x = - \dfrac{7}{2}\\
h) - {x^2} + x + 7\\
= - {x^2} + x - \dfrac{1}{4} + \dfrac{{29}}{4}\\
= - {\left( {x - \dfrac{1}{2}} \right)^2} + \dfrac{{29}}{4} \le \dfrac{{29}}{4}\\
\Leftrightarrow GTLN = \dfrac{{29}}{4},khi\,x = \dfrac{1}{2}\\
k) - 13x + 25 - {x^2}\\
= - {x^2} - 13x - \dfrac{{169}}{4} + \dfrac{{269}}{4}\\
= - {\left( {x + \dfrac{{13}}{2}} \right)^2} + \dfrac{{269}}{4} \le \\
\Leftrightarrow GTLN = \dfrac{{269}}{4},khi\,x = \dfrac{{ - 13}}{2}
\end{array}$
