The function is .
Find the inflection points by equating the second derivative to zero.
\Apply first derivative on each side with respect to .
Apply second derivative on each side with respect to .
Determine the values of at which
or
does not exist.
The inflection points are and
.
Substitute in
.
Substitute in
.
Therefore the inflection points are and
.
Test for concavity in the intervals ,
and
.
Intervals | Test value | \
Sign of | Conclusion |
![]() | ![]() | ![]() | Concave upward |
![]() | \
| ![]() | Concave downward |
![]() | \
| ![]() | Concave upward |
The function is concave upward in the intervals and
.
The function is concave downward in the interval .
The inflection points are and
.
The function is concave upward in the intervals and
.
The function is concave downward in the interval .