Đáp án:$\left[ \begin{array}{l}
m = 1\\
- \frac{1}{2} < m < 1
\end{array} \right.$
Giải thích các bước giải:
$\begin{array}{l}
y = \left( {{m^2} - 1} \right){x^3} + \left( {m - 1} \right){x^2} - x + 4\\
\Rightarrow y' = 3\left( {{m^2} - 1} \right){x^2} + 2\left( {m - 1} \right)x - 1 < 0\forall x\\
\Rightarrow \left[ \begin{array}{l}
m = 1\\
\left\{ \begin{array}{l}
{m^2} - 1 < 0\\
\Delta ' < 0
\end{array} \right.
\end{array} \right. \Rightarrow \left[ \begin{array}{l}
m = 1\\
\left\{ \begin{array}{l}
- 1 < m < 1\\
{\left( {m - 1} \right)^2} + 3\left( {{m^2} - 1} \right) < 0
\end{array} \right.
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
m = 1\\
\left\{ \begin{array}{l}
- 1 < m < 1\\
{m^2} - 2m + 1 + 3{m^2} - 3 < 0
\end{array} \right.
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
m = 1\\
\left\{ \begin{array}{l}
- 1 < m < 1\\
- \frac{1}{2} < m < 1
\end{array} \right.
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
m = 1\\
- \frac{1}{2} < m < 1
\end{array} \right.
\end{array}$
