Final answer:
A relative maximum cannot occur at a hole because the function must be defined at that point to be considered for a relative maximum, and a hole represents a point where the function is not defined.
Step-by-step explanation:
In mathematics, a relative maximum is a point where a function has a local peak; that is, the function's value at this point is higher than (or equal to) the function’s values at nearby points. However, a relative maximum cannot occur at a hole, which is a point where the function is not defined. A hole in the graph of a function represents a discontinuity, and for a point to be considered a relative maximum, the function must be defined at that point, which means it has an actual output value there.
In summary, the concept of a relative maximum requires that the function's value at a certain point is greater than the values of the function at points in some open interval around it, which cannot be true at a hole.