# Thread: Find the critical points of...

1. ## Find the critical points of...

Find the critical points of...

$x^3+x^2+2\alpha{x}(y+1)+y^2+2y$

And classify them for $|\alpha|> 1$ and $|\alpha| < 1$, where $\alpha \in \mathbb{R}$

2. Originally Posted by Mozart
Find the critical points of...

$x^3+x^2+2\alpha{x}(y+1)+y^2+2y$

And classify them for $|\alpha|> 1$ and $|\alpha| < 1$, where $\alpha \in \mathbb{R}$
Okay,
1) What are "critical points"?

2) If that definition involves derivatives, what are the derivatives of that function with respect to x and y?