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I am having major difficulties with two Differential equation.

1. If I have the equation P=2000/(1+9e^.06t). where p=population and t=time. How do I work out when the population is growing the fastest? To work this question out do I just make t the subject and diff twice and let it equal to zero?

2. The diff equation dp/dt= .08p(1-p/1000)(1-200/p) has an inital population of Po how do I show that the population is increasing if 200<P<1000 and decreasing if 0<P<200.

Please help

Thanx:)