(a)
(b)
(c)
(a)
where the integral is the area of the triangle with height 1 and base 1;
So the function f(x) has a local maximum at (1,2), a point of inflection at (2,1.2),
and a local minimum at (3,0.4) where we have rounded to one decimal place
when necessary.
In Figure N6–11b, the graph of f is shown again, but now it incorporates the
information just obtained using the FTC.
Example 29 __
Readings from a car’s speedometer at 10-minute intervals during a 1-hour period
are given in the table; t = time in minutes, v = speed in miles per hour:
Draw a graph that could represent the car’s speed during the hour.
Approximate the distance traveled, using L(6), R(6), and T(6).
Draw a graph that could represent the distance traveled during the hour.SOLUTIONS:
Any number of curves will do. The graph has only to pass through the points
given in the table of speeds, as does the graph in Figure N6–12a.