Ta có \(A=\frac{4x-3x^2}{x^2+1}\)\(\Rightarrow\)A-1=\(\frac{4x-3x^2}{x^2+1}-1\)=\(\frac{4x-4x^2-1}{x^2+1}\)=\(\frac{-\left(4x^2-4x+1\right)}{x^2+1}=\frac{-\left(2x-1\right)^2}{x^2+1}\)\(\le0\)
dấu''='' xảy ra \(\Leftrightarrow-\left(2x-1\right)^2=0\Leftrightarrow2x-1=0\Leftrightarrow x=\frac{1}{2}\)
vạy max A-1=0khi x=1/2 suy ra max A =1 khi x=1/2