Monotonicity from the Derivative

Monotonicity from the Derivative

If:

$$f'(x)\geq0$$

throughout an interval, then $$f(x)$$ is non-decreasing there.

If:

$$f'(x)\leq0$$

throughout an interval, then $$f(x)$$ is non-increasing there.

Usage

- Used to determine monotonic behaviour when the derivative may vanish at some points.