Definition
1. Given any x1 & x2 from an interval I with x1 < x2 if f ( x1 ) < f ( x2 ) then f ( x ) is increasing on I.
2. Given any x1 & x2 from an interval I with x1 < x2 if f ( x1 ) > f ( x2 ) then f ( x ) is decreasing on I.
This definition will in fact be utilized in the proof of the next fact in this section.
The Given fact summarizes up what we were doing in the previously
Fact
1. If f ′ ( x ) = 0 for each x on some interval I, then f ( x) is increasing on the interval.
2. If f ′ ( x ) = 0 for each x on some interval I, then f (x ) is decreasing on the interval.
3. If f ′ ( x ) = 0 for each x on some interval I, then f ( x ) is constant on the interval.