toán 11 GTNN-GTLN

P

pesaubuon98

y=[tex]sin^2x -2cos^2x +1= sin^2x-2(1-sin^2x)+1 = 3sin^2x-1 [/tex]
Ta có 0 \leq [tex]sin^2x [/tex] \leq 1
<=> 0 \leq [tex]3sin^2x [/tex] \leq 3
<=> -1 \leq [tex]3sin^2x-1 [/tex] \leq 2
Vậy Min=-1 , Max=2
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D

demon311

2)

$0 \le |\cos 3x| \le 1 \\
-2 \le |\cos 3x|-2 \le -1 \\
Min \ y=-2 \Leftrightarrow \cos 3x=0 \Leftrightarrow 3x=\dfrac{ \pi}{2}+k\pi \Leftrightarrow x=\dfrac{ \pi}{6}+\dfrac{ k\pi}{3} \\
Max \ y=-1 \Leftrightarrow \cos 3x=\pm 1 \Leftrightarrow 3x=k\pi \Leftrightarrow x=\dfrac{ k\pi}{3} \\$
 
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