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,
for
an integer. (We found the zeros of sine in this exercise, Apostol Section 2.8 Exercise #1.)
-
is increasing if
and decreasing if
.
- Taking the second derivative,
Thus,
is increasing if
and decreasing if
.
- We sketch the curve,
Second derivative should be 2cos2x (not -2cos2x). The rest of the answer is correct.