Barrons AP Calculus

(a)

(b)

(c)

(d)

(a)

(b)

(c)

(d)

(a)

SOLUTIONS: See Figure N6–19b.

f(b)    −   f(a)    =   length  of  RQ.

.

    average value   of  f   over    [a,b]   =   length  of  CD, where   CD  ·   AB  or

CD  ·   (b  −   a)  is  equal   to  the area    F(b)    −   F(a).

Example 41 __

The graph in Figure N6–20 shows the speed v(t) of a car, in miles per hour, at
10-minute intervals during a 1-hour period.

Give    an  upper   and a   lower   estimate    of  the total   distance    traveled.

When    does    the acceleration    appear  greatest?

Estimate    the acceleration    when    t   =   20.

Estimate    the average speed   of  the car during  the interval    30  ≤   t   ≤   50.

Figure  N6–20

SOLUTIONS:

A   lower   estimate,   using   minimum speeds  and     hr  for 10  min,    is

.

This    yields      mi  for the total   distance    traveled    during  the hour.   An  upper