\color{red}a =
\color{blue}b =
Below we have the slope field of an ODE
y' = F(y) with three stationary solutions.
Let \color{teal}y be solution
with \color{teal}y(X) = Y and
domain ]\, {\color{red}a}\, ,\, {\color{blue}b}\,[.
Determine {\color{red}a} and {\color{blue}b}.
Write "infty" for +\infty and "-infty" for -\infty.
\color{red}a =
\color{blue}b =
The slope field shows at a point (x_0,y_0) a tiny piece of the tangent
of a solution of the ODE, on which (x_0,y_0) lies.
The slope of the tangent is determined by the value of the right-hand side of the ODE with the values (x_0,y_0).
We have three stationary solutions y_{\infty, 1}=C,
y_{\infty, 2}=A, y_{\infty, 3}=B.
A solution remains within a strip.
But it is {\color{teal}y(X) = Y} > B unbounded,
i.e.
\color{red}a = B and \color{blue}b = +\infty.
But it is {\color{teal}y(X) = Y} < C unbounded,
i.e.
\color{red}a = - \infty and \color{blue}b = C.
It is A < {\color{teal}y(X) = Y} < B and thus
\color{red}a = A and \color{blue}b = B.
It is C < {\color{teal}y(X) = Y} < A and thus
\color{red}a = C and \color{blue}b = A.