Question

Tìm gtln của

A= -2x² + 6x - 12

Answer 1

\(A=-2x^2+6x-12\)

\(=-2\left(x^2-3x+\dfrac{9}{4}\right)-\dfrac{15}{2}\)

\(=-2\left(x-\dfrac{3}{2}\right)^2-\dfrac{15}{2}\le-\dfrac{15}{2}\)

\(maxA=-\dfrac{15}{2}\Leftrightarrow x=\dfrac{3}{2}\)

Answer 2

Ta có: \(A=-2x^2+6x-12\)

\(=-2\left(x^2-3x+6\right)\)

\(=-2\left(x^2-2\cdot x\cdot\dfrac{3}{2}+\dfrac{9}{4}+\dfrac{15}{4}\right)\)

\(=-2\left(x-\dfrac{3}{2}\right)^2-\dfrac{15}{2}\le-\dfrac{15}{2}\forall x\)

Dấu '=' xảy ra khi \(x=\dfrac{3}{2}\)