\[y = x² + x \cdot \frac{|x + 1|}{x + 1} - 6\]
\[y = \left\{ \begin{matrix} x² + x - 6,\ \ x + 1 > 0 \\ x² - x - 6,\ \ x + 1 < 0 \\ \end{matrix} \right.\ \]
\[x > - 1:\]
\[y = x^{2} + x - 6;\ \ \ ветви\ вверх;\]
\[\ x_{0} = - \frac{1}{2};\ \ y_{0} = - 6\frac{1}{4};\ \ \ \]
\[y( - 1) = - 6.\]
\[x < - 1:\]
\[y = x^{2} - x - 6;\ \ \ ветви\ вверх;\]
\[x_{0} = \frac{1}{2};\ \ \ y_{0} = - 6\frac{1}{4};\ \ \ \ \]
\[y( - 1) = - 4.\]