\(y'=x^2+2\left(m+3\right)x+4\left(m+3\right)\)
\(y'=0\Rightarrow x^2+2\left(m+3\right)x+4\left(m+3\right)=0\) (1)
(1) có 2 nghiệm phân biệt thỏa mãn \(x_1< x_2< -1\) khi:
\(\left\{{}\begin{matrix}\Delta'=\left(m+3\right)^2-4\left(m+3\right)>0\\\left(x_1+1\right)\left(x_2+1\right)>0\\\dfrac{x_1+x_2}{2}< -1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(m+3\right)\left(m-1\right)>0\\x_1x_2+x_1+x_2+1>0\\x_1+x_2< -2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(m+3\right)\left(m-1\right)>0\\-2\left(m+3\right)+4\left(m+3\right)+1>0\\-2\left(m+3\right)< -2\end{matrix}\right.\)
\(\Rightarrow m>1\)
Có 8 giá trị nguyên của m
