The First Derivative Test
Let c be a critical number of a function f which is continuous on the open interval I containing c. If f is differentiable on the interval, except possibly at c, then f(c) can be classified as follows
1. If f '(x) changes from negative to positive at c then f has a relative minimum at (c,f(c))
2. If f '(x) changes from positive to negative at c then f had a relative maximum at (c,f(c))
3. If f '(x) is both positive or both negative around c then f(c) is neither a relative minimum or relative maximum.