One+that+deals+with+both+derivatives+and+the+definite+integral

1. You will have to use your calculator for part c; remember that it is fnInt(function, x, lower limit of integration, upper limit of integration) Mimi: a) This means R(6) must be > 0. By plugging in 6 for t into the above equation, you get R(6) = 4.438 and therefore the number of mosquitoes is increasing at t = 6. b) Take the derivative to see if the function is increasing at a decreasing rate. R'(t) = (5sqrt(t))(-sin(t/5)(1/5) + (1/10sqrt(t))(cos(t/5)), and R'(6) = -1.913. Because R'(6) < 0, the number of mosquitoes is increasing at a decreasing rate. c) To find the quantity of mosquitoes, you need to take the integral of the given function. 1000 + integral R(t) dt = 964.335, so approximately 964 mosquitoes.