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| PAGE: 184 | SET: Exercises | PROBLEM: 49 |
(a)
The function is 
over the interval 
.
Apply derivative on each side with respect to 
.
(b)
Graph :
Graph the function and its derivative.
(c)
Find the critical numbers by applying derivative.
Equate its derivative to 
.
Therefore the critical numbers are 
and 
.
(d)
Consider the test intervals to find the interval of increasing and decreasing.
Test intervals are 
, 
and 
.
| Test interval | Test value | Sign of  |
Conclusion |
 |
 |
|
Decreasing |
 |
 |
|
Increasing |
 |
 |
|
Decreasing |
The function 
is increasing on the interval .
is positive on the interval .
The function is decreasing on the intervals and .
is negative on the intervals and .
(a)
.
(b)
(c)
Critical numbers are and .
(d)
is positive on the interval .
is negative on the intervals and .
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