\(B=5x-x^2+9\)
\(=-\left(x^2-5x+\dfrac{25}{4}\right)+\dfrac{11}{4}\)
\(=\dfrac{11}{4}-\left(x-\dfrac{5}{2}\right)^2\)
Nhận xét :
\(\left(x-\dfrac{5}{2}\right)^2\ge0\)
\(\Leftrightarrow-\left(x-\dfrac{5}{2}\right)^2\le0\)
\(\Leftrightarrow\dfrac{11}{4}-\left(x-\dfrac{5}{2}\right)^2\le\dfrac{11}{4}\)
\(\Leftrightarrow B\le\dfrac{11}{4}\)
Dấu "=" xảy ra khi : \(x=\dfrac{5}{2}\)
Vậy \(B_{Max}=\dfrac{11}{4}\Leftrightarrow x=\dfrac{5}{2}\)
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