Step 1:
\The function is
.
Differentiate with respect to
.

Find the critical number by equating
to zero.

Step 2:
\Critical point is
.
Since the function is cube root function, So we do not consider negative values of
.
Test intervals are
.
| Interval | \Test Value | \Sign of ![]() | \
Conclusion | \
![]() | \
![]() | \
\
\
| \
Decreasing | \
![]() | \
![]() | \
\
\
| \
Increasing | \
Thus, the function is decreasing on the interval
and increasing on the interval
.
Solution:
\The function
is increasing on interval
.
\
\
\
\