Cho hàm số $y=\dfrac{\cos x+2}{10\cos x-m}$. Xác định $m$ để hàm...

Đặt \)">t=\cos x\Rightarrow y=\dfrac{t+2}{10t-m}\Rightarrow {y}'=\dfrac{-m-20}{{{\left( 10t-m \right)}^{2}}}x\in \left( \dfrac{\pi }{3};\dfrac{\pi }{2} \right)t\in \left( 0;\dfrac{1}{2} \right)y=\dfrac{\cos x+2}{10\cos x-m}\left( \dfrac{\pi }{3};\dfrac{\pi }{2} \right)y=\dfrac{t+2}{10t-m}\left( 0;\dfrac{1}{2} \right)\Leftrightarrow {y}'<0,\forall t\in \left( 0;\dfrac{1}{2} \right)\Leftrightarrow \dfrac{m+20}{{{\left( 10t-m \right)}^{2}}}\le 0,\forall t\in \left( 0;\dfrac{1}{2} \right)\Leftrightarrow \left\{ \begin{aligned}
& m+20<0 \\
& \dfrac{m}{10}\notin \left( 0;\dfrac{1}{2} \right) \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& m=-20 \\
& m\notin \left( 0;5 \right) \\
\end{aligned} \right.\Leftrightarrow m<-20$.