The function is
.
Apply first derivative with respect to
.




Apply second derivative with respect to
.






Determine the values of
at which
or
does not exist.

Simplify the expression.
\


or 
Solve for
.



Solve for
.

Here the values of
is in imaginary, so does not consider it.
The values of
are
and
.
Test for concavity in the intervals
,
and
.
| Intervals | \Test value | \ \
Sign of | \
Conclusion | \
![]() | \
\
| \
![]() | \
Concave downward | \
![]() | \
\
| \
![]() | \
Concave upward | \
![]() | \
\
| \
![]() | \
Concave downward | \
\
The function is concave downward in the intervals
and
.
The function is concave upward in the interval
.