FIGURE N6–19b
SOLUTIONS: See Figure N6–19b.
(a) f (b) − f (a) = length RQ.
(b) = slope of secant PQ.
(c) F(b) − F(a) = = area of APDQB.
(d) = 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.
(a) Give an upper and a lower estimate of the total distance traveled.
(b) When does the acceleration appear greatest?
(c) Estimate the acceleration when t = 20.
(d) Estimate the average speed of the car during the interval 30 ≤ t ≤ 50.
FIGURE N6–20
SOLUTIONS:
(a) 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 estimate uses