Question

y=log₂(x³-3x²+m). Tìm m để hàm số xác định trên (1;3)

Answer 1

\(\Leftrightarrow x^3-3x^2+m>0\) ; \(\forall x\in\left(1;3\right)\)

\(\Leftrightarrow x^3-3x^2>-m\) ; \(\forall x\in\left(1;3\right)\)

Xét hàm \(f\left(x\right)=x^3-3x^2\) trên \(\left(1;3\right)\)

\(f'\left(x\right)=3x^2-6x=0\Rightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\)

\(\Rightarrow\min\limits_{\left(1;3\right)}f\left(x\right)=f\left(2\right)=-4\)

\(\Rightarrow m< -4\)