Take the system $x' = -3x+x^{2} , \quad y' = 7y$.

How many critical points does the system have? .

What is the critical point with the largest x-coordinate?
( , ).

The linearization at this point is $\begin{bmatrix} u \\ v \end{bmatrix} ' = A \begin{bmatrix} u \\ v \end{bmatrix}$ where $A$ is
$A = {}$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$

At this point the behavior is
For behavior write one of "saddle", "source", "sink", "spiral sink", "spiral source", "center".