có ai 2k2 giống tui ko
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Câu 45:
Đặt \(g\left(x\right)=\frac{x}{x^2+x+1}-\frac{m}{3}\)
\(g'\left(x\right)=\left(\frac{x}{x^2+x+1}\right)'=\frac{-x^2+1}{\left(x^2+x+1\right)^2}\)
\(g'\left(x\right)=0\Rightarrow x=\pm1\), \(g'\left(x\right)\)xác định với mọi \(x\inℝ\).
Suy ra để hàm số \(f\left(x\right)=\left|g\left(x\right)\right|\)có \(4\)điểm cực trị thì phương trình \(g\left(x\right)=0\)có hai nghiệm phân biệt khác \(\pm1\).
\(g\left(x\right)=0\Leftrightarrow\frac{x}{x^2+x+1}=\frac{m}{3}\)
\(lim_{x\rightarrow-\infty}\frac{x}{x^2+x+1}=0,lim_{x\rightarrow+\infty}\frac{x}{x^2+x+1}=0\)
\(g\left(-1\right)=-1,g\left(1\right)=\frac{1}{3}\)
Suy ra BBT của hàm \(\frac{x}{x^2+x+1}\).
Từ đó suy ra để phương trình \(\frac{x}{x^2+x+1}\)có hai nghiệm phân biệt thì
\(\orbr{\begin{cases}0< \frac{m}{3}< \frac{1}{3}\\-1< \frac{m}{3}< 0\end{cases}}\Leftrightarrow m\in\left\{-2,-1\right\}\)(vì \(m\)nguyên)
Chọn A.
hăh hăh hăh
em k10
kb ko cj
kb chứ sợ gì