The function is
.
Apply derivative on each side with respect to
.

Quotient rule of derivative:
.

.

Apply derivative on each side with respect to
.



.
Find Inflection points.
\
To find the inflection points of the function
.


Inflection point occurs at
.
Subtitute
in the function.

Inflection point is
.
Test intervals
and
.
| Intervals | \Test value | \ \
Sign of | \
Conclusion | \
![]() | \
![]() | \
\
| \
Concave downward | \
![]() | \
\
| \
![]() | \
Concave upward | \
The function is concave up in the interval
.
The function is concave down in the interval
.
The function is concave up in the interval
.
The function is concave down in the interval
.
Inflection point is
.