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,
- Since
when
and
when
we have
is decreasing if
and
is increasing if
.
- Taking the second derivative,
Since this is positive for all
, this means
is increasing for all
.
- We sketch the curve,