Step 1 :
\Increasing or decreasing test :
\(a) If
on an interval, then f is increasing on that interval.
(b) If
on an interval, then f is decreasing on that interval.
Step 2 :
\The function is
.
The critical points exist when
.
Equate
to zero :

The critical points are
and
.
Consider the test intervals :
and
.
| Interval | \Test Value | \ | \
| \
| \
Sign of ![]() | \
Conclusion | \
| \
| \
+ | \ | \
+ | \ \
| \
Decreasing | \
| \
![]() | \
+ | \![]() | \
+ | \ \
| \
Decreasing | \
| \
![]() | \
+ | \+ | \+ | \ \
| \
Increasing | \
| \
![]() | \
+ | \+ | \+ | \ \
| \
Increasing | \
Thus, The function is increasing on the intervals
and
.
Combine above two intervals.
\Hence, the function is increasing on the interval
.
Solution :
\The function is increasing on the interval
.