In Lesson 4.2.3 you should have noticed a close relationship between derivatives and integrals just like with velocity and distance. In particular, you have seen that if you know the velocity,
in miles per hour, how far has the car traveled after hours? After hours? After hours?
For the first 2 hours:
See the homework help for problem 4-99.
How far did the car travel between
In Chapter 3 you considered the instantaneous rate of change (derivative) of any function. Explain why you expect the derivative,
, of a distance function of a car to be the velocity function, , of the car.
Since s is a distance function, what does the slope of a distance function represent?