(a)
\The function is .
Find the critical numbers by applying derivative.
\Apply derivative on each side with respect to .
Equate the derivative to .
Critical number is .
(b)
\Consider the test intervals to find the interval of increasing and decreasing.
\Test intervals are and
.
Test interval | \Test value | \Sign of ![]() | \
Conclusion | \
![]() | \
![]() | \
\
| \
Increasing | \
![]() | \
![]() | \
\
| \
Increasing | \
The function is increasing on the intervals
and
.
(c)
\Use first derivative test to identify all relative extrema.
\The function is increasing function so it does not have any exreme points.
\(d)
\Graph the function is .
(a)
\Critical number is .
(b)
\The function is increasing on the intervals
and
.
(c)
\Does not have any exreme points.
\(d)
\Graph of the function is .