Strict Monotonicity Using Derivative

Strict Monotonicity Using Derivative

If:

$$f'(x)\geq0$$

throughout an interval and $$f'(x)$$ is not identically zero on any subinterval, then $$f(x)$$ is strictly increasing.

Similarly, if:

$$f'(x)\leq0$$

throughout an interval and $$f'(x)$$ is not identically zero on any subinterval, then $$f(x)$$ is strictly decreasing.

Usage

- Useful when the derivative becomes zero at isolated points but the function remains strictly monotonic.