Suppose that a bee is flying around and at time t=0, the bee spots a delicious flower and starts buzzing around it excitedly. As the bee buzzes around, let s(t) give the height (in centimeters) of the bee above or below the flower at time t (measured in seconds). For instance, s(0)=0.981, which means that at time t=0, the bee is 0.981 cm above the flower.
a) Compute the average velocity of the bee on the following time intervals.
[0.5,1]
[1,1.5]
[0.75,1.25]
[0.9,1]
[1,1.1]
[0.95,1.05]
[0.99,1]
[1,1.01]
[0.995,1.005]
b) Of the 9 average velocities computed, which do you think gives the best estimate of the instantaneous velocity of the bee at time t=1?
c) Compute an even better estimate of the instantaneous velocity of the bee at time t=1.
d) Estimate the instantaneous velocity of the bee at t=4. What does this value tell you about the movement of the bee at the instant t=4?