Calculus
posted by jessica on .
Could someone explain this question please.
Suppose the population (in thousands of a certain species of insect after t months is described by the function p(t)=4t+ (100t)/(t^2+400) + 500. Determine the maximum population in the first three months.

when x is small (as in the interval [0,3]
100t/(t^2+400) is just basically t/4
so, p(t) looks a lot like 4t + t/4 + 500
that's just a line, so the max and min are at the ends of the interval. 
If I factor it out, it'll be 17t/4 + 500.
then plug in 3
17(3)/4+500=512 x 1000
=512,750.
therefore the population would be 512,750?