Which term refers to values in a function where the derivative does not exist?

The term that refers to values in a function where the derivative does not exist is critical points. Critical points are significant in calculus because they are the values of the independent variable (typically x) where the function's behavior can change; these can be points where the function has a local maximum, local minimum, or an inflection point.

At a critical point, the derivative either equals zero or is undefined. This includes scenarios such as sharp corners, vertical tangents, or points where the function is not differentiable due to discontinuities. Understanding critical points helps in analyzing the behavior of functions and is essential for finding extrema in various applications.

While the other terms have specific meanings related to the behavior of functions, they do not directly define locations where the derivative does not exist. Inflection points indicate where the function changes its concavity, and local maxima and global minima are specific types of critical points where the function reaches high or low values. However, critical points encompass a broader range of situations, including those where the derivative may be undefined, making it the most appropriate choice for this question.