Đáp án:
\(m < -3\)
Giải thích các bước giải:
\[\begin{array}{l}
y = \left( {m - 4} \right){x^4} + \left( {m + 3} \right){x^2} - m + 1\\
\Rightarrow y' = 4\left( {m - 4} \right){x^3} + 2\left( {m + 3} \right)x\\
\Rightarrow y' = 0\\
\Leftrightarrow 4\left( {m - 4} \right){x^3} + 2\left( {m + 3} \right)x = 0\,\,\,\,\left( * \right)\\
\Leftrightarrow 2x\left[ {2\left( {m - 4} \right){x^2} + m + 3} \right] = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x = 0\\
g\left( x \right) = 2\left( {m - 4} \right){x^2} + m + 3 = 0\,\,\,\,\left( 1 \right)
\end{array} \right.\\
\Rightarrow hs\,\,\,co\,\,3\,\,cuc\,\,tri \Leftrightarrow \left( * \right)\,\,\,co\,\,\,3\,\,nghiem\,\,pb\\
\Leftrightarrow \left( 1 \right)\,\,co\,\,\,2\,\,\,nghiem\,\,pb\,\,\, \ne 0\\
\Leftrightarrow \left\{ \begin{array}{l}
m - 4 \ne 0\\
- m - 3 > 0\\
m + 3 \ne 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
m \ne 4\\
m < - 3\\
m \ne - 3
\end{array} \right. \Leftrightarrow m < - 3.
\end{array}\]
