Let
- Find all points such that
;
- Determine the intervals on which
is monotonic by examining the sign of
;
- Determine the intervals on which
is monotonic by examining the sign of
;
- Sketch the graph of
.
- We take the derivative,
Thus,
-
is increasing if
or
and
is decreasing if
or
. (We have to take some care here to leave out the points
and
since the function is not defined at these points.)
- Taking the second derivative,
Thus,
is increasing for
and
and
is decreasing for
.
- We sketch the curve,