a. If is constant, then the derivative 0, which means we would have
as constant solutions.
Next, we have 4 possible intervals to consider where the derivative doesn't vanish:
- for , we have (consider the sign of the derivative for, say, );
- for , we have ;
- for , we have ;
- and for , we have
Taking all these facts together, we see that ...
b. is increasing on the interval , and
c. is decreasing on the interval .