### Home > APCALC > Chapter 4 > Lesson 4.2.5 > Problem 4-100

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*

If

in miles per hour, how far has the car traveled afterhours? After hours? After hours?For the first 2 hours:

See the homework help for problem 4-99.

How far did the car travel between

and hours? 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?