58. Distance Function The graph gives a sales representative's distance from his home as a function of time on a certain day. (a) Determine the time intervals on which his distance from home was increasing and those on which it was decreasing. (b) Describe in words what the graph indicates about his travels on this day. (c) Find the net change in his distance from home between noon and 1:00 P.M. Distance from home (miles) 8 A.M. 10 2 4. 6 PM. NOON Time (hours)
58. Distance Function The graph gives a sales representative's distance from his home as a function of time on a certain day. (a) Determine the time intervals on which his distance from home was increasing and those on which it was decreasing. (b) Describe in words what the graph indicates about his travels on this day. (c) Find the net change in his distance from home between noon and 1:00 P.M. Distance from home (miles) 8 A.M. 10 2 4. 6 PM. NOON Time (hours)
58. Distance Function The graph gives a sales representative's distance from his home as a function of time on a certain day. (a) Determine the time intervals on which his distance from home was increasing and those on which it was decreasing. (b) Describe in words what the graph indicates about his travels on this day. (c) Find the net change in his distance from home between noon and 1:00 P.M. Distance from home (miles) 8 A.M. 10 2 4. 6 PM. NOON Time (hours)
Changing Water Levels The graph shows the depth of water W in a reservoir over a one-year period as a function of the number of days x since the beginning of the year. (a) Determine the intervals on which the function W is increasing and on which it is decreasing. (b) At what value of x does W achieve a local maximum? A local minimum? (c) Find the net change in the depth W from 100 days to 300 days.
Transcribed Image Text:58. Distance Function The graph gives a sales representative's
distance from his home as a function of time on a certain day.
(a) Determine the time intervals on which his distance from
home was increasing and those on which it was
decreasing.
(b) Describe in words what the graph indicates about his
travels on this day.
(c) Find the net change in his distance from home between
noon and 1:00 P.M.
Distance
from home
(miles)
8 A.M.
10
2
4.
6 PM.
NOON
Time (hours)
Formula Formula A function f ( x ) is also said to have attained a local minimum at x = a , if there exists a neighborhood ( a − δ , a + δ ) of a such that, f ( x ) > f ( a ) , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a f ( x ) − f ( a ) > 0 , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a In such a case f ( a ) is called the local minimum value of f ( x ) at x = a .
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