a, A=-x^2 -11x+7 =-(x^2 +11x -7) = -(x^2 +11x +121/4) +149/4 >= 149/4
A(max)=149/4 tại x=-11/2
b: Ta có: \(-5x^2+7x+8\)
\(=-5\left(x^2-\dfrac{7}{5}x-\dfrac{8}{5}\right)\)
\(=-5\left(x^2-2\cdot x\cdot\dfrac{7}{10}+\dfrac{49}{100}-\dfrac{209}{100}\right)\)
\(=-5\left(x-\dfrac{7}{10}\right)^2+\dfrac{209}{20}\le\dfrac{209}{20}\forall x\)
Dấu '=' xảy ra khi \(x=\dfrac{7}{10}\)
a: Ta có: \(-x^2-11x+7\)
\(=-\left(x^2+11x-7\right)\)
\(=-\left(x^2+2\cdot x\cdot\dfrac{11}{2}+\dfrac{121}{4}-\dfrac{149}{4}\right)\)
\(=-\left(x+\dfrac{11}{2}\right)^2+\dfrac{149}{4}\le\dfrac{149}{4}\forall x\)
Dấu '=' xảy ra khi \(x=-\dfrac{11}{2}\)
c: Ta có: \(-7x^2+8x+15\)
\(=-7\left(x^2-\dfrac{8}{7}x-\dfrac{15}{7}\right)\)
\(=-7\left(x^2-2\cdot x\cdot\dfrac{4}{7}+\dfrac{16}{49}-\dfrac{121}{49}\right)\)
\(=-7\left(x-\dfrac{4}{7}\right)^2+\dfrac{121}{7}\le\dfrac{121}{7}\forall x\)
Dấu '=' xảy ra khi \(x=\dfrac{4}{7}\)
