Answer
a) The intervals when his distance from home is increasing are (8 a.m., 9 a.m.), (10 a.m., NOON), and (3 p.m., 5 p.m.)
The intervals when his distance from home is decreasing are (1 p.m., 3 p.m.) and (6 p.m., 7 p.m.)
b) From 8 a.m. to 9 a.m., he was traveling from home to someplace and stayed there for an hour. Then he traveled again for two hours and arrived at noon at some other place even further from home than the last one. He was having lunch and at 1 p.m., he was going back home. Unfortunately for the guy, at 3 p.m. he had a call from his boss and had to go to another place which was pretty far from home. He arrived at 5 p.m. and stayed there for an hour. Finally, he was free to go home. The traffic was pretty fast, so he managed to arrive home at 7 p.m.
c) The net change is zero.
Work Step by Step
a) A function decreases when the slope is negative. While a function increases when the slope is positive.
b) All the analysis was made by checking when the function increases, decreases, and stays the same (when the slope is zero).
c) We can see that the slope is zero, so there isn't any change in distance. Thus, the net change is zero.
