Toán Lớp 11: Tìm GTNN,GTLN của hàm số:
y=3sin^2 x-2
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Toán Lớp 11: Tìm GTNN,GTLN của hàm số:
y=3sin^2 x-2
Comments ( 2 )
GTNN:y = – 2\,khi:x = k\pi \\
GTLN:y = 1\,khi:x = \dfrac{\pi }{2} + k\pi
\end{array} \right.$
y = 3{\sin ^2}x – 2\\
Do: – 1 \le \sin x \le 1\\
\Leftrightarrow 0 \le {\sin ^2}x \le 1\\
\Leftrightarrow 0 \le 3{\sin ^2}x \le 3\\
\Leftrightarrow – 2 \le 3{\sin ^2}x – 2 \le 1\\
\Leftrightarrow – 2 \le y \le 1\\
\Leftrightarrow \left\{ \begin{array}{l}
GTNN:y = – 2\,khi:x = k\pi \\
GTLN:y = 1\,khi:x = \dfrac{\pi }{2} + k\pi
\end{array} \right.
\end{array}$