Question

Tìm GTNN, hay GTLN của \(-6x^2-x+7\) .

Answer 1

GTLN = -6(x² + 1/12) + 7 + 1/144 = 7\(\dfrac{1}{144}\)

Answer 2

\(A=-6x^2-x+7\)

\(=-6\left(x^2+\frac{1}{6}x-\frac{7}{6}\right)\)

\(=-6\left[\left(x^2+\frac{1}{6}x+\frac{1}{144}\right)-\frac{169}{144}\right]\)

\(=-6\left[\left(x+\frac{1}{12}\right)^2-\frac{169}{144}\right]\)

\(=\frac{169}{24}-6\left(x+\frac{1}{12}\right)^2\le\frac{169}{24}\)

Vậy GTLN của A là \(\frac{169}{24}\) khi \(\left(x+\frac{1}{12}\right)^2=0\Leftrightarrow x=-\frac{1}{12}\)