A Cepheid variable star is a star whose brightness alternately increases and decreases. The most easily visible such star is Delta Cepheid, for which the interval between times of maximum brightness is 5.4 days. The average brightness of this star is 4.0 and its brightness changes by ±0.35. In view of these data, the brightness of Delta Cepheid at time t, where is measured in days, has been modeled by the function
(a) Find the rate of change of the brightness after days.
(b) Find, correct to two decimal places, the rate of increase after one day.