Barrons AP Calculus - David Bock

maximum speeds; it equals

or 55 mi for the total distance.
(b) The acceleration, which is the slope of v(t), appears greatest at t = 5 min, when the curve is
steepest.
(c) To estimate the acceleration v ′(t) at t = 20, we approximate the slope of the curve at t = 20.
The slope of the tangent at t = 20 appears to be equal to (10 mph)/(10 min) = (10 mph)/ =
60 mi/hr^2.
(d) The average speed equals the distance traveled divided by the time. We can approximate the
distance from t = 30 to t = 50 by the area under the curve, or, roughly, by the sum of the areas
of a rectangle and a trapezoid:

Thus the average speed from t = 30 to t = 50 is

EXAMPLE 42

Given the graph of G(x) in Figure N6–21a, identify the following if G ′(x) = g(x):
(a) g(b)
(b)

(c)

(d)

FIGURE N6–21a

FIGURE N6–21b