Barrons AP Calculus

(b)

(c)

(d)

(a)
(b)

(c)

(d)

estimate    uses    maximum speeds; it  equals

or  55  mi  for the total   distance.

The acceleration,   which   is  the slope   of  v(t),   appears greatest    at  t   =   5   min,

when    the curve   is  steepest.

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  =   

.

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):

g(b)

.