Question

1.Tìm GTNN,GTLN của E = \(\dfrac{3-4x}{2x^2+2}\)

Answer 1

\(E=\dfrac{\left(x-2\right)^2-\left(x^2+1\right)}{2\left(x^2+1\right)}\)\(=\dfrac{\left(x-2\right)^2}{2\left(x^2+1\right)}-\dfrac{1}{2}\ge\dfrac{-1}{2}\)

Vậy E_min=\(\dfrac{-1}{2}\Leftrightarrow x=2\)

\(E=\dfrac{4x^2+4-4x-1-4x^2}{2\left(x^2+1\right)}\)\(=2-\dfrac{4x^2+4x+1}{2\left(x^2+1\right)}\)=\(2-\dfrac{\left(x+\dfrac{1}{2}\right)^2}{2\left(x^2+1\right)}\le2\)

Vậy E_max=2\(\Leftrightarrow x=\dfrac{-1}{2}\)