(a)
\The function is
over
.
Apply derivative with respect to
.

(b)
\Graph :
\Graph the function
and its derivative
.

(c)
\The function is
.
Find the critical numbers by applying derivative .
\
Equate it to zero.
\
The critical numbers are
and
.
(d)
\Consider the test intervals to find the interval of increasing and decreasing in
.
Test intervals are
,
,
and
.
| Test interval | \Test value | \Sign of ![]() | \
Conclusion | \
![]() | \
![]() | \
\
| \
Increasing | \
![]() | \
![]() | \
\
| \
\
Decreasing \ | \
![]() | \
![]() | \
\
| \
Increasing | \
![]() | \
![]() | \
\
| \
Decreasing | \
is positive on the intervals
and
.
is negative on the interval
and
.
(a) The differentiation of the function is
.
(b)
\
(c) Critical numbers are
and
.
(d)
\
is positive on the intervals
and
.
is negative on the interval
and
.