Under what conditions are there more than one equilibrium? $a = $

Are there any conditions for which there are no equilibria? yes no

We have two special cases that are missed by the above two conditions.

Under what conditions are there more than one equilibrium? $b = $ and $c=$

Under what conditions are there no equilibria? $b = $ and $c \ne$

We have some special cases that are missed by the above conditions.

What conditions on the slope of the tangent line will give you an unstable equilibrium? The equilibrium $E$ will be unstable if $f'(E) \gt $ or $f'(E) \lt $ .

To reiterate, the critical quantity is the slope of the tangent line or the derivative value of $f$ evaluated at $x=$ .