Recall, we proved that a function can have local maximum/minimum at only critical points. However, not every critical poling is a point of local maximum/minimum.

Let

Then, both and exist at every point and

,

imply that is the only cortical point. But at , has no local maximum for

Also, does not have a local at minimum at since

Thus, in other words, in every neighborhood of , there is a curve in the domain at every point of which takes value bigger than , and also there exists another curve in the domain of at every point of which takes value less than