Toán Lớp 11: Tìm GTLN và GTNN
a/ y=4-7sinx
b/ y=2sinx-5
c/ y=5-2cosx
d/ y=3cosx+4
e/ y=(3√cosx)+2
f/ y =2IsinxI-4
Leave a reply
Register Now
Login
Lost Password
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Toán Lớp 11: Tìm GTLN và GTNN
a/ y=4-7sinx
b/ y=2sinx-5
c/ y=5-2cosx
d/ y=3cosx+4
e/ y=(3√cosx)+2
f/ y =2IsinxI-4
Comments ( 1 )
a)y = 4 – 7\sin x\\
Do: – 1 \le \sin x \le 1\\
\Leftrightarrow – 7 \le – 7\sin x \le 7\\
\Leftrightarrow – 3 \le 4 – 7\sin x \le 11\\
\Leftrightarrow – 3 \le y \le 11\\
\Leftrightarrow GTNN:y = – 3\,;GTLN:y = 11\\
b)y = 2\sin x – 5\\
– 2 \le 2\sin x \le 2\\
\Leftrightarrow – 7 \le 2\sin x – 5 \le – 3\\
\Leftrightarrow – 7 \le y \le – 3\\
\Leftrightarrow \left\{ \begin{array}{l}
GTNN:y = – 7\\
GTLN:y = – 3
\end{array} \right.\\
d)y = 3\cos x + 4\\
– 3 \le 3\cos x \le 3\\
\Leftrightarrow 1 \le 3\cos x + 4 \le 7\\
\Leftrightarrow 1 \le y \le 7\\
\Leftrightarrow \left\{ \begin{array}{l}
GTNN:y = 1\\
GTLN:y = 7
\end{array} \right.\\
e)y = \left( {3\sqrt {\cos x} } \right) + 2\\
0 \le 3\sqrt {\cos x} \le 3\\
\Leftrightarrow 2 \le y \le 5\\
\Leftrightarrow \left\{ \begin{array}{l}
GTNN:y = 2\\
GTLN:y = 5
\end{array} \right.\\
f)y = 2\left| {\sin x} \right| – 4\\
0 \le 2\left| {\sin x} \right| \le 2\\
\Leftrightarrow – 4 \le 2\left| {\sin x} \right| – 4 \le – 2\\
\Leftrightarrow – 4 \le y \le – 2\\
\Leftrightarrow \left\{ \begin{array}{l}
GTNN:y = – 4\\
GTLN:y = – 2
\end{array} \right.
\end{array}$