Maximum/Minimum Problems
Local maximum and minimum
In , we define an open disk centered at with radius , denoted by , to be the set of all points such that their distance from is smaller than . Then we have the following definition:
Definition: Suppose be a function of two variables. has a local maximum (minimum) at if
for all in the domain of in an open disk for some .
The intuitive meaning of local maximum (minimum) of at is that attains the greatest (smallest) value of among all other points in the domain "close enough" to .