Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)
so that for or . The derivative being equal to 0 gives you some information about the long-term stability of the population ; namely, that the carrying capacity is 1000.
b. If , then and , so that , which means the population would be increasing.
c. If , then but , so and the population would be decreasing.