FIGURE N6–18
SOLUTIONS:
(1) (d), since acceleration is the derivative of velocity and in (d) v ′, the slope, is constant.
(2) (e), when t = 0 the slope of this v-curve (which equals acceleration) is greatest.
(3) (b), since for this car the net distance traveled (given by the net area) equals zero.
(4) (e), since the area under the v-curve is greatest, this car is farthest east.
(5) (e), the average velocity equals the total distance divided by 6, which is the net area divided
by 6 (see (4)).
(6) (a), since only for this car is the net area negative.
(7) (a) again, since net area is negative only for this car.
EXAMPLE 40
Identify each of the following quantities for the function f (x), whose graph is shown in Figure
N6–19a (note: F ′(x) = f (x)):
(a) f (b) − f (a)
(b)
(c) F(b) − F(a)
(d)
FIGURE N6–19a