Decreasing Function

A function decreases on an interval if for all , where . If for all , the function is said to be strictly decreasing.

Conversely, a function increases on an interval if for all with . If for all , the function is said to be strictly increasing.

If the derivative of a continuous function satisfies on an open interval , then is decreasing on . However, a function may decrease on an interval without having a derivative defined at all points. For example, the function is decreasing everywhere, including the origin , despite the fact that the derivative is not defined at that point.

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