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
.