Toán tìm GTNN,GTLN của hàm y = sin^4 (x) + cos^4(x)… giúp em với ạ 02/08/2021 By Parker tìm GTNN,GTLN của hàm y = sin^4 (x) + cos^4(x)… giúp em với ạ
$y=\sin^4x+\cos^4x$ $=(\sin^2x+\cos^2x)^2-2\sin^2x\cos^2x$ $=1-\dfrac{1}{2}.4\sin^2x\cos^2x$ $=1-\dfrac{\sin^22x}{2}$ $=1-\dfrac{1-\cos4x}{4}$ $=\dfrac{3}{4}+\dfrac{1}{4}\cos4x$ $-1\le \cos 4x\le 1$ $\Rightarrow \dfrac{1}{2}\le y\le 1$ $\to y_{\min}=\dfrac{1}{2}; y_{\max}=1$ Trả lời
$y=\sin^4x+\cos^4x$
$=(\sin^2x+\cos^2x)^2-2\sin^2x\cos^2x$
$=1-\dfrac{1}{2}.4\sin^2x\cos^2x$
$=1-\dfrac{\sin^22x}{2}$
$=1-\dfrac{1-\cos4x}{4}$
$=\dfrac{3}{4}+\dfrac{1}{4}\cos4x$
$-1\le \cos 4x\le 1$
$\Rightarrow \dfrac{1}{2}\le y\le 1$
$\to y_{\min}=\dfrac{1}{2}; y_{\max}=1$