The function is .
Observe the graph :
\The function is increasing on the intervals
and
The function is decreasing on the interval
and
.
Find open interval analytically.
\Apply derivative to find the critical numbers.
\Equate it to zero .
\The critical points are and
.
Test intervals are ,
,
and
.
Test intervals | Test value | Sign of ![]() | Conclusion |
![]() | ![]() | ![]() | Decreasing |
![]() | ![]() | ![]() | Increasing |
![]() | ![]() | ![]() | Decreasing |
![]() | ![]() | ![]() | Increasing |
The function is increasing on the intervals
and
The function is decreasing on the interval
and
.
The function is increasing on the intervals
and
The function is decreasing on the interval
and
.