cuc tri luong giac

Question

Tim GTNN:

${A=sin^{4} x+\cos^{7} x}$

score 0 · Answer 1

Khuyến mãi cho cái

$\max$

Ta luôn có

$\sin^2 x \ge \sin^4 x$ vì

$\sin^2 x (1-\sin^2 x) \ge 0$

$\cos^2 x \ge \cos^7 x$ vì

$\cos^2 x(1-\cos^ 5 x) \ge 0$

Vạy

$\sin^2 x +\cos^2 x =1 \ge \sin^4 x +\cos^7 x$

$\max A = 1$ dấu

$=$ xảy ra

$\Leftrightarrow x=k2\pi$ hoặc

$x=-\dfrac{\pi}{2} +k2\pi$ với

$k\in Z$

tu dung duk khuyen mai, suong ghe, hi – Gió! 31-10-13 09:08 PM

score 1 · Answer 2

Ta có:

$\sin^4x\ge0;\cos^7x\ge-1$

$\Rightarrow A\ge-1$ .

$\min A=-1 \Leftrightarrow \left\{\begin{array}{l}\sin x=0\\\cos x=-1\end{array}\right. \Leftrightarrow x=-\pi+k2\pi,k\in\mathbb{Z}$

2 Đáp án