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iceghost

$7x-2x^2 \\
=-2(x^2-\dfrac72x) \\
=-2(x^2-2.x.\dfrac74+\dfrac{49}{16}-\dfrac{49}{16}) \\
=-2[(x-\dfrac74)^2-\dfrac{49}{16}) \\
=-2(x-\dfrac74)^2+\dfrac{49}8 \le \dfrac{49}8 \\
\implies Max = \dfrac{49}8 \iff x-\dfrac74=0 \iff x=\dfrac74$
 
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