What do we call the maximum or minimum points of a function based on its first derivative?

The maximum or minimum points of a function, which are determined by analyzing the first derivative, are known as critical points. To find these points, we set the first derivative of the function equal to zero or identify where it does not exist. At critical points, the function may change from increasing to decreasing (indicating a maximum) or from decreasing to increasing (indicating a minimum).

In contrast, inflection points refer to locations on the graph where the function changes concavity, which is not necessarily related to the maximum or minimum values. Endpoints are simply the values at the ends of a given interval for a function but do not involve the behavior of the function’s derivative. Asymptotes relate to the behavior of a function as it approaches certain values, typically representing lines that the function approaches but never crosses, which is also unrelated to maximum or minimum points. Therefore, the critical points are the specific features we focus on when identifying maxima and minima of a function via its first derivative.