(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
.