Toán Lớp 8: Tìm giá trị lớn nhất của: F = 5 – 4x^2 + 4 ; G= -4x^2+8x-2003
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Toán Lớp 8: Tìm giá trị lớn nhất của: F = 5 – 4x^2 + 4 ; G= -4x^2+8x-2003
HELP MEEEEEEEEEEE!!!!!!
Comments ( 2 )
a)\quad \max F = 6 \Leftrightarrow x = \dfrac12\\
b)\quad \max G = -1999 \Leftrightarrow x = 1
\end{array}\)
a)\quad F =5 – 4x^2 + 4x\\
\to F = -(4x^2 – 4x + 1) + 6\\
\to F = – (2x – 1)^2 + 6\\
\text{Ta có:}\\
\quad (2x-1)^2\geqslant 0\quad \forall x\\
\to – (2x-1)^2 \leqslant 0\\
\to – (2x-1)^2 +6\leqslant 6\\
\to F \leqslant 6\\
\text{Dấu = xảy ra} \Leftrightarrow 2x – 1 =0\Leftrightarrow x = \dfrac12\\
\text{Vậy}\ \max F = 6 \Leftrightarrow x = \dfrac12\\
b)\quad G = -4x^2 +8x – 2003\\
\to G = -4(x^2 – 2x + 1) – 1999\\
\to G = -4(x-1)^2 – 1999\\
\text{Ta có:}\\
\quad (x-1)^2\geqslant 0\quad \forall x\\
\to – 4(x-1)^2 \leqslant 0\\
\to – 4(x-1)^2 -1999\leqslant -1999\\
\to G\leqslant -1999\\
\text{Dấu = xảy ra}\ \Leftrightarrow x – 1= 0\Leftrightarrow x = 1\\
\text{Vậy}\ \max G = -1999 \Leftrightarrow x = 1
\end{array}\)