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