Question

Tìm GTNN của các đa thưcs sau

a, f(x) =(x-2) (x+1)

b, g(x) = ( 2x-1 )(x-3)

c, h(x) =(2x-3)(x-3)+1

Answer 1

a) \(f\left(x\right)=\left(x-2\right)\left(x+1\right)\)

\(=x^2+x-2x-2\)

\(=x^2-x-2\)

\(=x^2-\dfrac{1}{2}x-\dfrac{1}{2}x-2\)

\(=x^2-\dfrac{1}{2}x-\dfrac{1}{2}x+\dfrac{1}{4}-\dfrac{9}{4}\)

\(=\left(x-\dfrac{1}{2}\right)^2-\dfrac{9}{4}\)

Vì \(\left(x-\dfrac{1}{2}\right)^2\ge0\Rightarrow\left(x-\dfrac{1}{2}\right)^2-\dfrac{9}{4}\ge\dfrac{-9}{4}\)

Dấu "=" xảy ra khi \(\left(x-\dfrac{1}{2}\right)^2=0\)

\(\Rightarrow x=\dfrac{1}{2}\)

Vậy \(Min_{f\left(x\right)}=\dfrac{-9}{4}\) khi \(x=\dfrac{1}{2}.\)

Answer 2

Mấy câu kia tương tự nhé!