Suppose that f is continuous on [a, b] and differentiable on (a, b).

If f’ > 0 on (a, b), then f is increasing on [a, b].

If f’ ³ 0 on (a, b), then f is nondecreasing on [a, b].

If f’ < 0 on (a, b), then f is decreasing on [a, b].

If f’ £ 0 on (a, b), then f is nonincreasing on [a, b].

If f’ = 0 on (a, b), then f is constant on [a, b].