Question

Giúp mik nhanh vơi Tìm GTNN, GTLN y= căn 1+cos4x -2

Answer 1

\(y=\sqrt{1+cos4x}-2\)

+) \(y=\sqrt{1+cos4x}-2\ge-2\)

\(\Rightarrow min=-2\Leftrightarrow cos4x=-1\Leftrightarrow4x=\pi+k2\pi\Leftrightarrow x=\dfrac{\pi}{4}+\dfrac{k\pi}{2}\)

+) \(cos4x\in\left[-1;1\right]\Rightarrow1+cos4x\le2\Rightarrow y=\sqrt{1+cos4x}-2\le\sqrt{2}-2\)

\(\Rightarrow max=\sqrt{2}-2\Leftrightarrow cos4x=1\Leftrightarrow4x=k2\pi\Leftrightarrow x=\dfrac{k\pi}{2}\)