# Not the First Derivative Test

The "Not the First Derivative Test" is very simple, and it's intuitive, this just puts it into words.

### If f'(x) > 0 for all x in (a,b), then f is increasing on [a,b]

### If f'(x) < 0 for all x in (a,b), then f is decreasing on [a,b]

If f'(x) = 0 for all x in (a,b), then f is constant on [a,b]

# The First Derivative Test

The First Derivative Test says that given a critical point, where the derivative is 0 or und.,

### If f'(x) changes from negative to positive at c, then f is a relative minimum at (c, f(c)).

### If f'(x) changes from positive to negative at c, then f is a relative maximum at (c, f(c)).

If f'(x) is positive or negative on both sides of c, then it doesn't mean anything.

David Witten