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 .