Toán Lớp 10: Y= 4 √(sinx+3) -1
( -1 ngoài căn ạ) tìm gtnn gtln
mn giúp em với
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Toán Lớp 10: Y= 4 √(sinx+3) -1
( -1 ngoài căn ạ) tìm gtnn gtln
mn giúp em với
Comments ( 1 )
GTNN:y = 4\sqrt 2 – 1\,khi:x = \dfrac{{ – \pi }}{2} + k2\pi \\
GTLN:y = 7\,khi:x = \dfrac{\pi }{2} + k2\pi
\end{array} \right.$
y = 4\sqrt {\sin x + 3} – 1\\
Do: – 1 \le \sin x \le 1\\
\Leftrightarrow 2 \le \sin x + 3 \le 4\\
\Leftrightarrow \sqrt 2 \le \sqrt {\sin x + 3} \le 2\\
\Leftrightarrow 4\sqrt 2 \le 4\sqrt {\sin x + 3} \le 8\\
\Leftrightarrow 4\sqrt 2 – 1 \le y \le 7\\
Vậy\,\left\{ \begin{array}{l}
GTNN:y = 4\sqrt 2 – 1\,khi:x = \dfrac{{ – \pi }}{2} + k2\pi \\
GTLN:y = 7\,khi:x = \dfrac{\pi }{2} + k2\pi
\end{array} \right.
\end{array}$