Chapter 9.4, Problem 21E

(a)

To determine

To show: The differential equation is increasing and decreasing for given condition:

Solution is increasing if $m<P<M$.

Solution is decreasing if $0<P<m$.

(b)

To determine

To draw: The direction field for given data.

(c)

To determine

To solve: The differential equation $\frac{dP}{dt}=kP\left(1-\frac{P}{M}\right)\left(1-\frac{m}{P}\right)$.

(d)

To determine

To show: The solution is extinct for $P_0<m$.