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 for all
since
for all
.
- Taking the second derivative,
Thus,
is increasing for
and decreasing for
.
- We sketch the curve,
You get a better understanding of this function if you increase the domain to e.g. (-20,20).