\(A=\frac{x}{\left(x+2019\right)^2}\)
Với \(x\le0\Rightarrow A\le0\)
Với \(x>0\Rightarrow A=\frac{x}{x^2+4038x+2019^2}=\frac{1}{x+\frac{2019^2}{x}+4038}\)
\(\Rightarrow A\le\frac{1}{2\sqrt{x.\frac{2019^2}{x}}+4038}=\frac{1}{8076}\)
\(\Rightarrow A_{max}=\frac{1}{8076}\) khi \(x=2019\)