\
\
\
Step 1 :
\(a)
\The function .
Differentiate with respect to x.
\Determination of critical points :
\The function is undefined when
.
Equate to zero:
The critical points are and
.
Step 2 :
\Consider test intervals as and
.
Interval | \Test Value | \Sign of ![]() | \
Conclusion | \
![]() | \
![]() | \
\
| \
Increasing | \
![]() | \
![]() | \
\
| \
Decreasing | \
![]() | \
![]() | \
\
| \
Decreasing | \
![]() | \
![]() | \
\
| \
Increasing | \
Thus, The function is increasing on the intervals and
.
And The function is decreasing on the intervals and
.
Solution :
\\
The function is increasing on the intervals and
.
The function is decreasing on the intervals and
.