Question

Tìm GTLN:

a) A= -3x^2-6x-4

b) B= -5x^2+7x-3

c) C= -1/2x^2-x-1

Answer 1

\(A=-3\left(x^2+2x+1\right)-1=-3\left(x+1\right)^2-1\le-1\)

\(A_{max}=-1\) khi \(x=-1\)

\(B=-5\left(x^2-2.\frac{7}{10}x+\frac{49}{100}\right)-\frac{11}{20}=-5\left(x-\frac{7}{10}\right)^2-\frac{11}{20}\le-\frac{11}{20}\)

\(B_{max}=-\frac{11}{20}\) khi \(x=\frac{7}{10}\)

\(C=-\frac{1}{2}\left(x^2+2x+1\right)-\frac{1}{2}=-\frac{1}{2}\left(x+1\right)^2-\frac{1}{2}\le-\frac{1}{2}\)

\(C_{max}=-\frac{1}{2}\) khi \(x=-1\)