A Cepheid variable star is a star whose brightness alternately increases and decreases. For a certain star, the interval between times of maximum brightness is4.4days. The average brightness of this star is2.0and its brightness changes by0.45. Using this information, the brightness of the star at timet, wheretis measured in days, has been modeled by the function

B(t) =2.0+0.45sin(2t/4.4)

a) Find the rate of change of the brightness at timetdays.

dB/dt=

b) Find the rate of change of brightness at timet=4days.

dB/dt=