\(A=-3x^2+2x-5=-3\left(x^2-\frac{2}{3}x+\frac{5}{3}\right)\)
\(=-3\left(x^2-2.x.\frac{1}{3}+\frac{1}{9}-\frac{1}{9}+\frac{5}{3}\right)\)
\(=-3\left[\left(x-\frac{1}{3}\right)^2+\frac{14}{9}\right]\)
\(=-3\left(x-\frac{1}{3}\right)^2-\frac{14}{3}\)
\(\Rightarrow A_{min}=-\frac{14}{3}\Leftrightarrow-3\left(x-\frac{1}{3}\right)^2=0\)
\(\Leftrightarrow\left(x-\frac{1}{3}\right)^2=0\Rightarrow x=\frac{1}{3}\)
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