a) $y = x^3 - 6x^2 + 9x$
$TXĐ: D = R$
$y' = 3x^2 - 12x + 9$
$y' = 0 \Leftrightarrow x^2 - 4x + 3 = 0 \Leftrightarrow \left[\begin{array}{l}x = 1\\x =3\end{array}\right.$
Bảng xét dấu:
$\begin{array}{|l|cr|}
\hline
x & -\infty & & &1& & & & 3& && +\infty\\
\hline
y & &+& &0& &-& &0&& +& \\
\hline
\end{array}$
b) $y = \dfrac{1}{2}x^4 - 3x^2 - 3$
$TXĐ: D= R$
$y' = 2x^3 - 6x$
$y' = 0 \Leftrightarrow x^3 - 3x = 0 \Leftrightarrow \left[\begin{array}{l}x = 0\\x =\pm \sqrt{3}\end{array}\right.$
Bảng xét dấu:
$\begin{array}{|l|cr|}
\hline
x & -\infty & & &-\sqrt{3} & && & 0& &&\sqrt{3}&&& +\infty\\
\hline
y & &-& &0&& +& &0&& -&0&&+ \\
\hline
\end{array}$
c) $y = \dfrac{2x - 5}{x - 3}$
$TXĐ: D = R\backslash \left\{3\right\}$
$y' = \dfrac{-1}{(x-3)^2} <0, \forall x \ne 3$
Bảng xét dấu:
$\begin{array}{|l|cr|}
\hline
x & -\infty & & &3&&& +\infty\\
\hline
y & &-& &||&& - \\
\hline
\end{array}$
