Chapter 1.2, Problem 34P

In addition to the Gompertz equation (see Problem 33) another equation used to model the growth of cancerous tumors is the Bertalanffy equation

$\frac{dV}{dt}=a{V}^{2/3}-bV$,

Where $a$ and $b$ are positive constants. This model assumes that the tumor grows at a rate proportional to surface area, while the loss of tumor mass due to cell death is proportional to the volume of the tumor. Sketch the graph of $f\left(V\right)$ verses $V$, find the critical points, and determine whether each is asymptotically stable or unstable.