calculus
posted by Anon .
for 0<=t<=21 the rate of change of the number of blakc flies on a coastal island at time t days is modeled by R(t)=3sqrt(t)cos(t/3) flies per day. There are 500 flies on the island at the time t=0. To the nearest whole #, what is the max # of flies for 0<=t<=21?

R = 3√t cos(t/3)
R' = 3/2√t cos(t/3)  √t sin(t/3)
R' = 0 when
3/2√t cos(t/3) = √t sin(t/3)
3cos(t/3) = 2t sin(t/3)
3/2 cot(t/3) = t
t = 1.96, 9.88, 19.08
not sure how there are 500 flies at t=0. That doesn't fit R(t). Anyway, if that can be fixed, just plug in those values for t to get what you need. 
wait..dont u hve to integrate it?

oops. yes. I misread the problem. Didn't see the "rate of change" phrase.

wait..so how would you integrate that equation..im hving trouble with tht..

Beats me. It doesn't use standard elementary functions. Are you studying numerical methods?