[tex]g'(x)=\frac{x+1}{\sqrt{x^2+2x+2}}f'(\sqrt{x^2+2x+2})[/tex]
[tex]g'(x)=0\Leftrightarrow \left[\begin{array}{l} x+1=0\\\sqrt{x^2+2x+2}=1\\\sqrt{x^2+2x+2}=3 \end{array}\right.\\\Leftrightarrow \left[\begin{array}{l} x=-1\\x=2\sqrt{2}-1\\x=-1-2\sqrt{2} \end{array}\right.[/tex]
$
\begin{array}{c|ccccccccc}
x & -\infty & & -1-2\sqrt{2} & & -1 & & 2\sqrt{2}-1 & & +\infty \\
\hline
g'(x) & & - & 0 & + & 0 & - & 0 & +
\end{array}
$
Chọn A