Toán Lớp 12: Tìm m để HS y=x³ -6x² +3(m+2)x -m-6 có 2 cực trị cùng dấu
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Toán Lớp 12: Tìm m để HS y=x³ -6x² +3(m+2)x -m-6 có 2 cực trị cùng dấu
Comments ( 2 )
y = {x^3} – 6{x^2} + 3\left( {m + 2} \right)x – m – 6\\
\Leftrightarrow y’ = 3{x^2} – 12x + 3\left( {m + 2} \right)
\end{array}$
y’ = 0\\
\Leftrightarrow 3{x^2} – 12x + 3\left( {m + 2} \right) = 0\\
\Leftrightarrow {x^2} – 4x + m + 2 = 0\left( * \right)
\end{array}$
\Leftrightarrow \left\{ \begin{array}{l}
\Delta ‘ > 0\\
{x_1} + {x_2} > 0\\
{x_1}{x_2} > 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
4 – m – 2 > 0\\
4 > 0\\
m + 2 > 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
m < 2\\
m > – 2
\end{array} \right.\\
\Leftrightarrow – 2 < m < 2\\
Vậy\, – 2 < m < 2
\end{array}$