Derivative Criterion for One-to-One Function

Derivative Criterion for One-to-One Function

If:

$$f'(x)>0$$

throughout an interval, then $$f$$ is one-to-one there.

Similarly, if:

$$f'(x)<0$$

throughout an interval, then $$f$$ is one-to-one there.

Usage

- Used to establish injectivity and the existence of an inverse function.