Using function derivative to judge function monotonicity It is known that: in general, if f '(x) is zero at a finite number of points in an interval and is positive (or negative) at the other points, then f (x) is still monotonically increasing (or decreasing) in the interval. Correct. Is it correct if f' (x) does not exist at a finite number of points in an interval?

Using function derivative to judge function monotonicity It is known that: in general, if f '(x) is zero at a finite number of points in an interval and is positive (or negative) at the other points, then f (x) is still monotonically increasing (or decreasing) in the interval. Correct. Is it correct if f' (x) does not exist at a finite number of points in an interval?

Incorrect, non differentiable description, there may be breakpoints, which can be understood as mutation, so it will not be monotonous