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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, , at time then you can compute the distance traveled from to by using .

  1. If 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.

  2. How far did the car travel between and hours?

  3. 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?