The notation "f'" represents the derivative of a function f with respect to its variable. It measures how the function's output changes as its input changes, providing insight into the function's rate of change at any given point. Derivatives are fundamental in calculus and are used in various applications, including physics and engineering. In practical terms, if f describes the position of an object over time, then f' indicates the object's velocity. A positive value of f' means the function is increasing, while a negative value indicates it is decreasing. Understanding derivatives helps analyze trends and behaviors in various fields.