Final answer:
A 'find the location of the local extremum' calculator determines the maximum and minimum points of a function (local extrema). These are points where the function reaches a peak or valley compared to nearby points.
Step-by-step explanation:
The question "What does a 'find the location of the local extremum' calculator determine?" revolves around analyzing a mathematical function to find specific values known as local extrema. A local extremum refers to points on a graph where a function reaches a local maximum or minimum value; that is, a point where the function's value is higher (in the case of a maximum) or lower (in the case of a minimum) than that of any nearby points.
To clarify the options presented:
- Points where the function is not continuous would refer to discontinuities, which are not necessarily related to local extrema.
- Maximum and minimum points of the function are exactly what a calculator designed to find local extrema would look for, as these points signify where the function peaks or valleys locally.
- Values that make the function equal to zero are known as the function's roots or zeros, which are different from extrema unless the extremum occurs at a value of zero.
- The domain and range of the function describe the input and output values of the function, respectively, which also do not directly relate to the concept of extremum.
Given these explanations, the correct option for what such a calculator determines is B) Maximum and minimum points of the function.